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<H1 class=3DfirstHeading id=3DfirstHeading>Real number</H1>
<DIV id=3DbodyContent>
<H3 id=3DsiteSub>From Wikipedia, the free encyclopedia</H3>
<DIV id=3DcontentSub></DIV>
<DIV id=3Djump-to-nav>Jump to: <A=20
href=3D"http://en.wikipedia.org/wiki/Real_number#column-one">navigation</=
A>, <A=20
href=3D"http://en.wikipedia.org/wiki/Real_number#searchInput">search</A><=
/DIV><!-- start content -->
<P>In <A title=3DMathematics=20
href=3D"http://en.wikipedia.org/wiki/Mathematics">mathematics</A>, the =
<B>real=20
numbers</B> may be described informally in several different ways. The =
real=20
numbers include both <A title=3D"Rational number"=20
href=3D"http://en.wikipedia.org/wiki/Rational_number">rational =
numbers</A>, such=20
as 42 and =E2=88=9223/129, and <A title=3D"Irrational number"=20
href=3D"http://en.wikipedia.org/wiki/Irrational_number">irrational =
numbers</A>,=20
such as <A title=3DPi href=3D"http://en.wikipedia.org/wiki/Pi">pi</A> =
and the <A=20
class=3Dmw-redirect title=3D"Square root of two"=20
href=3D"http://en.wikipedia.org/wiki/Square_root_of_two">square root of =
two</A>;=20
or, a real number can be given by an infinite <A title=3D"Decimal =
representation"=20
href=3D"http://en.wikipedia.org/wiki/Decimal_representation">decimal=20
representation</A>, such as 2.4871773339..., where the digits continue =
in some=20
way; or, the real numbers may be thought of as points on an infinitely =
long <A=20
title=3D"Number line" =
href=3D"http://en.wikipedia.org/wiki/Number_line">number=20
line</A>.</P>
<P>These descriptions of the real numbers, while intuitively accessible, =
are not=20
sufficiently rigorous for the purposes of pure mathematics. The =
discovery of a=20
suitably rigorous definition of the real numbers =E2=80=94 indeed, the =
realisation that=20
a better definition was needed =E2=80=94 was one of the most important =
developments of=20
19th century mathematics. Popular definitions in use today include <A=20
title=3D"Equivalence class"=20
href=3D"http://en.wikipedia.org/wiki/Equivalence_class">equivalence =
classes</A> of=20
<A title=3D"Cauchy sequence"=20
href=3D"http://en.wikipedia.org/wiki/Cauchy_sequence">Cauchy =
sequences</A> of=20
rational numbers; <A title=3D"Dedekind cut"=20
href=3D"http://en.wikipedia.org/wiki/Dedekind_cut">Dedekind cuts</A>; a =
more=20
sophisticated version of "decimal representation"; and an axiomatic =
definition=20
of the real numbers as the unique <A class=3Dmw-redirect =
title=3D"Complete space"=20
href=3D"http://en.wikipedia.org/wiki/Complete_space">complete</A> <A=20
title=3D"Archimedean property"=20
href=3D"http://en.wikipedia.org/wiki/Archimedean_property">Archimedean</A=
> <A=20
title=3D"Order theory"=20
href=3D"http://en.wikipedia.org/wiki/Order_theory">ordered</A> <A=20
title=3D"Field (mathematics)"=20
href=3D"http://en.wikipedia.org/wiki/Field_(mathematics)">field</A>. =
These=20
definitions are all described in detail below.</P>
<P>The term "real number" is a <A title=3DRetronym=20
href=3D"http://en.wikipedia.org/wiki/Retronym">retronym</A> coined in =
response to=20
"<A title=3D"Imaginary number"=20
href=3D"http://en.wikipedia.org/wiki/Imaginary_number">imaginary =
number</A>".<SUP=20
class=3D"noprint Template-Fact"=20
title=3D"This claim needs references to reliable sources from August =
2008"=20
style=3D"WHITE-SPACE: nowrap">[<I><A title=3D"Wikipedia:Citation needed" =

href=3D"http://en.wikipedia.org/wiki/Wikipedia:Citation_needed">citation =

needed</A></I>]</SUP></P>
<DIV class=3D"thumb tright">
<DIV class=3Dthumbinner style=3D"WIDTH: 302px"><A class=3Dimage=20
title=3D"Real numbers can be thought of as points on an infinitely long =
number line."=20
href=3D"http://en.wikipedia.org/wiki/File:Number-line.gif"><IMG =
class=3Dthumbimage=20
height=3D23 alt=3D""=20
src=3D"http://upload.wikimedia.org/wikipedia/commons/0/09/Number-line.gif=
"=20
width=3D300></A>=20
<DIV class=3Dthumbcaption>
<DIV class=3Dmagnify><A class=3Dinternal title=3DEnlarge=20
href=3D"http://en.wikipedia.org/wiki/File:Number-line.gif"><IMG =
height=3D11 alt=3D""=20
src=3D"http://en.wikipedia.org/skins-1.5/common/images/magnify-clip.png" =

width=3D15></A></DIV>Real numbers can be thought of as points on an =
infinitely=20
long <A title=3D"Number line"=20
href=3D"http://en.wikipedia.org/wiki/Number_line">number=20
line</A>.</DIV></DIV></DIV>
<TABLE class=3Dtoc id=3Dtoc summary=3DContents>
  <TBODY>
  <TR>
    <TD>
      <DIV id=3Dtoctitle>
      <H2>Contents</H2></DIV>
      <UL>
        <LI class=3Dtoclevel-1><A=20
        =
href=3D"http://en.wikipedia.org/wiki/Real_number#Basic_properties"><SPAN =

        class=3Dtocnumber>1</SPAN> <SPAN class=3Dtoctext>Basic =
properties</SPAN></A>=20

        <LI class=3Dtoclevel-1><A=20
        href=3D"http://en.wikipedia.org/wiki/Real_number#Uses"><SPAN=20
        class=3Dtocnumber>2</SPAN> <SPAN class=3Dtoctext>Uses</SPAN></A> =

        <LI class=3Dtoclevel-1><A=20
        href=3D"http://en.wikipedia.org/wiki/Real_number#History"><SPAN=20
        class=3Dtocnumber>3</SPAN> <SPAN =
class=3Dtoctext>History</SPAN></A>=20
        <LI class=3Dtoclevel-1><A=20
        =
href=3D"http://en.wikipedia.org/wiki/Real_number#Definition"><SPAN=20
        class=3Dtocnumber>4</SPAN> <SPAN =
class=3Dtoctext>Definition</SPAN></A>=20
        <UL>
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://en.wikipedia.org/wiki/Real_number#Construction_from_the_ra=
tional_numbers"><SPAN=20
          class=3Dtocnumber>4.1</SPAN> <SPAN =
class=3Dtoctext>Construction from the=20
          rational numbers</SPAN></A>=20
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://en.wikipedia.org/wiki/Real_number#Axiomatic_approach"><SPA=
N=20
          class=3Dtocnumber>4.2</SPAN> <SPAN class=3Dtoctext>Axiomatic=20
          approach</SPAN></A> </LI></UL>
        <LI class=3Dtoclevel-1><A=20
        =
href=3D"http://en.wikipedia.org/wiki/Real_number#Properties"><SPAN=20
        class=3Dtocnumber>5</SPAN> <SPAN =
class=3Dtoctext>Properties</SPAN></A>=20
        <UL>
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://en.wikipedia.org/wiki/Real_number#Completeness"><SPAN=20
          class=3Dtocnumber>5.1</SPAN> <SPAN =
class=3Dtoctext>Completeness</SPAN></A>=20

          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://en.wikipedia.org/wiki/Real_number#.22The_complete_ordered_=
field.22"><SPAN=20
          class=3Dtocnumber>5.2</SPAN> <SPAN class=3Dtoctext>"The =
complete ordered=20
          field"</SPAN></A>=20
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://en.wikipedia.org/wiki/Real_number#Advanced_properties"><SP=
AN=20
          class=3Dtocnumber>5.3</SPAN> <SPAN class=3Dtoctext>Advanced=20
          properties</SPAN></A> </LI></UL>
        <LI class=3Dtoclevel-1><A=20
        =
href=3D"http://en.wikipedia.org/wiki/Real_number#Generalizations_and_exte=
nsions"><SPAN=20
        class=3Dtocnumber>6</SPAN> <SPAN class=3Dtoctext>Generalizations =
and=20
        extensions</SPAN></A>=20
        <LI class=3Dtoclevel-1><A=20
        =
href=3D"http://en.wikipedia.org/wiki/Real_number#.22Reals.22_in_set_theor=
y"><SPAN=20
        class=3Dtocnumber>7</SPAN> <SPAN class=3Dtoctext>"Reals" in set=20
        theory</SPAN></A>=20
        <LI class=3Dtoclevel-1><A=20
        href=3D"http://en.wikipedia.org/wiki/Real_number#See_also"><SPAN =

        class=3Dtocnumber>8</SPAN> <SPAN class=3Dtoctext>See =
also</SPAN></A>=20
        <LI class=3Dtoclevel-1><A=20
        href=3D"http://en.wikipedia.org/wiki/Real_number#Notes"><SPAN=20
        class=3Dtocnumber>9</SPAN> <SPAN =
class=3Dtoctext>Notes</SPAN></A>=20
        <LI class=3Dtoclevel-1><A=20
        =
href=3D"http://en.wikipedia.org/wiki/Real_number#References"><SPAN=20
        class=3Dtocnumber>10</SPAN> <SPAN =
class=3Dtoctext>References</SPAN></A>=20
        <LI class=3Dtoclevel-1><A=20
        =
href=3D"http://en.wikipedia.org/wiki/Real_number#External_links"><SPAN=20
        class=3Dtocnumber>11</SPAN> <SPAN class=3Dtoctext>External =
links</SPAN></A>=20
        </LI></UL></TD></TR></TBODY></TABLE>
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<P><A id=3DBasic_properties name=3DBasic_properties></A></P>
<H2><SPAN class=3Deditsection>[<A title=3D"Edit section: Basic =
properties"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D1">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>Basic properties</SPAN></H2>
<P>A real number may be either <A title=3D"Rational number"=20
href=3D"http://en.wikipedia.org/wiki/Rational_number">rational</A> or <A =

title=3D"Irrational number"=20
href=3D"http://en.wikipedia.org/wiki/Irrational_number">irrational</A>; =
either <A=20
title=3D"Algebraic number"=20
href=3D"http://en.wikipedia.org/wiki/Algebraic_number">algebraic</A> or =
<A=20
title=3D"Transcendental number"=20
href=3D"http://en.wikipedia.org/wiki/Transcendental_number">transcendenta=
l</A>;=20
and either <A class=3Dmw-redirect title=3D"Positive number"=20
href=3D"http://en.wikipedia.org/wiki/Positive_number">positive</A>, <A=20
class=3Dmw-redirect title=3D"Negative number"=20
href=3D"http://en.wikipedia.org/wiki/Negative_number">negative</A>, or =
<A=20
title=3D"0 (number)" =
href=3D"http://en.wikipedia.org/wiki/0_(number)">zero</A>. Real=20
numbers are used to measure <A title=3D"Continuous function"=20
href=3D"http://en.wikipedia.org/wiki/Continuous_function">continuous</A> =

quantities. They may in theory be expressed by <A title=3D"Decimal =
representation"=20
href=3D"http://en.wikipedia.org/wiki/Decimal_representation">decimal=20
representations</A> that have an infinite sequence of digits to the =
right of the=20
decimal point; these are often represented in the same form as =
324.823122147=E2=80=A6=20
The <A title=3DEllipsis=20
href=3D"http://en.wikipedia.org/wiki/Ellipsis#In_mathematical_notation">e=
llipsis</A>=20
(three dots) indicate that there would still be more digits to come.</P>
<P>More formally, real numbers have the two basic properties of being an =
<A=20
title=3D"Ordered field" =
href=3D"http://en.wikipedia.org/wiki/Ordered_field">ordered=20
field</A>, and having the <A title=3D"Least upper bound axiom"=20
href=3D"http://en.wikipedia.org/wiki/Least_upper_bound_axiom">least =
upper=20
bound</A> property. The first says that real numbers comprise a <A=20
title=3D"Field (mathematics)"=20
href=3D"http://en.wikipedia.org/wiki/Field_(mathematics)">field</A>, =
with addition=20
and multiplication as well as division by nonzero numbers, which can be =
<A=20
title=3D"Total order" =
href=3D"http://en.wikipedia.org/wiki/Total_order">totally=20
order</A> on a number line in a way compatible with addition and =
multiplication.=20
The second says that if a nonempty set of real numbers has an <A=20
title=3D"Upper and lower bounds"=20
href=3D"http://en.wikipedia.org/wiki/Upper_and_lower_bounds">upper =
bound</A>, then=20
it has a <A title=3DSupremum =
href=3D"http://en.wikipedia.org/wiki/Supremum">least=20
upper bound</A>. These two together define the real numbers completely, =
and=20
allow its other properties to be deduced. For instance, we can prove =
from these=20
properties that every polynomial of odd degree with real coefficients =
has a real=20
root, and that if you add the square root of =E2=88=921 to the real =
numbers, obtaining=20
the <A title=3D"Complex number"=20
href=3D"http://en.wikipedia.org/wiki/Complex_number">complex =
numbers</A>, the=20
resulting field is <A title=3D"Algebraically closed field"=20
href=3D"http://en.wikipedia.org/wiki/Algebraically_closed_field">algebrai=
cally=20
closed</A>.</P>
<P><A id=3DUses name=3DUses></A></P>
<H2><SPAN class=3Deditsection>[<A title=3D"Edit section: Uses"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D2">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>Uses</SPAN></H2>
<P>In the physical sciences, most of the physical constants such as the=20
universal gravitational constant, and physical variables, such as =
position,=20
mass, speed, and electric charge, are modeled using real numbers. Note=20
importantly, however, that all actual measurements of physical =
quantities yield=20
<A title=3D"Rational number"=20
href=3D"http://en.wikipedia.org/wiki/Rational_number">rational =
numbers</A> due to=20
the (unavoidably) finite precision involved in the measurement.</P>
<P>Computers cannot directly operate on real numbers, but only on a =
finite=20
subset of rational numbers, limited by the number of bits used to store =
them.=20
However, <A title=3D"Computer algebra system"=20
href=3D"http://en.wikipedia.org/wiki/Computer_algebra_system">computer =
algebra=20
systems</A> are able to treat some <A title=3D"Irrational number"=20
href=3D"http://en.wikipedia.org/wiki/Irrational_number">irrational =
numbers</A>=20
exactly by storing their algebraic description (such as "sqrt(2)") =
rather than=20
their rational approximation.</P>
<P>A real number is said to be <I><A title=3D"Computable number"=20
href=3D"http://en.wikipedia.org/wiki/Computable_number">computable</A></I=
> if=20
there exists an algorithm that yields its digits. Because there are only =
<A=20
class=3Dmw-redirect title=3D"Countably infinite"=20
href=3D"http://en.wikipedia.org/wiki/Countably_infinite">countably</A> =
many=20
algorithms, but an uncountable number of reals, <A title=3D"Almost all"=20
href=3D"http://en.wikipedia.org/wiki/Almost_all">almost all</A> real =
numbers are=20
not computable. Some <A title=3D"Constructivism (mathematics)"=20
href=3D"http://en.wikipedia.org/wiki/Constructivism_(mathematics)">constr=
uctivists</A>=20
accept the existence of only those reals that are computable. The set of =
<A=20
class=3Dmw-redirect title=3D"Definable number"=20
href=3D"http://en.wikipedia.org/wiki/Definable_number">definable =
numbers</A> is=20
broader, but still only countable. If computers could use unlimited =
precision=20
real numbers (<A title=3D"Real computation"=20
href=3D"http://en.wikipedia.org/wiki/Real_computation">real =
computation</A>), then=20
one could solve <A title=3DNP-complete=20
href=3D"http://en.wikipedia.org/wiki/NP-complete">NP-complete</A> =
problems, and=20
even <A class=3Dmw-redirect title=3D"Sharp P"=20
href=3D"http://en.wikipedia.org/wiki/Sharp_P">#P</A>-complete problems =
in <A=20
title=3D"Polynomial time"=20
href=3D"http://en.wikipedia.org/wiki/Polynomial_time">polynomial =
time</A>,=20
answering affirmatively the <A title=3D"P =3D NP problem"=20
href=3D"http://en.wikipedia.org/wiki/P_%3D_NP_problem">P =3D NP =
problem</A>.=20
Unlimited precision real numbers in the physical universe are prohibited =
by the=20
<A title=3D"Holographic principle"=20
href=3D"http://en.wikipedia.org/wiki/Holographic_principle">holographic=20
principle</A> and the <A title=3D"Bekenstein bound"=20
href=3D"http://en.wikipedia.org/wiki/Bekenstein_bound">Bekenstein =
bound</A>.<SUP=20
class=3Dreference id=3Dcite_ref-0><A=20
href=3D"http://en.wikipedia.org/wiki/Real_number#cite_note-0"><SPAN>[</SP=
AN>1<SPAN>]</SPAN></A></SUP></P>
<P><SPAN id=3DR></SPAN>Mathematicians use the symbol <B>R</B> (or =
alternatively,=20
<IMG class=3Dtex alt=3D" \mathbb{R} "=20
src=3D"http://upload.wikimedia.org/math/6/9/a/69a45f1e602cd2b2c2e67e41811=
fd226.png">,=20
the letter "<A title=3DR href=3D"http://en.wikipedia.org/wiki/R">R</A>" =
in <A=20
title=3D"Blackboard bold"=20
href=3D"http://en.wikipedia.org/wiki/Blackboard_bold">blackboard =
bold</A>, Unicode=20
=E2=84=9D) to represent the <A title=3D"Set (mathematics)"=20
href=3D"http://en.wikipedia.org/wiki/Set_(mathematics)">set</A> of all =
real=20
numbers. The notation <B>R</B><SUP><I>n</I></SUP> refers to an =
<I>n</I>-<A=20
title=3DDimension =
href=3D"http://en.wikipedia.org/wiki/Dimension">dimensional</A>=20
space with real coordinates; for example, a value from =
<B>R</B><SUP>3</SUP>=20
consists of three real numbers and specifies a location in 3-dimensional =

space.</P>
<P>In mathematics, real is used as an adjective, meaning that the =
underlying=20
field is the field of real numbers. For example <I>real <A=20
title=3D"Matrix (mathematics)"=20
href=3D"http://en.wikipedia.org/wiki/Matrix_(mathematics)">matrix</A></I>=
, <I>real=20
<A title=3DPolynomial=20
href=3D"http://en.wikipedia.org/wiki/Polynomial">polynomial</A></I> and =
<I>real <A=20
title=3D"Lie algebra" =
href=3D"http://en.wikipedia.org/wiki/Lie_algebra">Lie=20
algebra</A></I>. As a substantive, the term is used almost strictly in =
reference=20
to the real numbers themselves (e.g., The "set of all reals").</P>
<P><A id=3DHistory name=3DHistory></A></P>
<H2><SPAN class=3Deditsection>[<A title=3D"Edit section: History"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D3">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>History</SPAN></H2>
<P><A class=3Dmw-redirect title=3D"Vulgar fraction"=20
href=3D"http://en.wikipedia.org/wiki/Vulgar_fraction">Vulgar =
fractions</A> had=20
been used by the <A title=3D"History of Egypt"=20
href=3D"http://en.wikipedia.org/wiki/History_of_Egypt">Egyptians</A> =
around 1000=20
BC; the <A class=3Dmw-redirect title=3D"Vedic civilization"=20
href=3D"http://en.wikipedia.org/wiki/Vedic_civilization">Vedic</A> "<A=20
class=3Dmw-redirect title=3D"Sulba Sutras"=20
href=3D"http://en.wikipedia.org/wiki/Sulba_Sutras">Sulba Sutras</A>" =
("rule of=20
chords" in, ca. 600 BC, include what may be the first 'use' of <A=20
title=3D"Irrational number"=20
href=3D"http://en.wikipedia.org/wiki/Irrational_number">irrational =
numbers</A>.=20
The concept of irrationality was implicitly accepted by early <A=20
title=3D"Indian mathematics"=20
href=3D"http://en.wikipedia.org/wiki/Indian_mathematics">Indian =
mathematicians</A>=20
since <A title=3DManava =
href=3D"http://en.wikipedia.org/wiki/Manava">Manava</A> (c.=20
750=E2=80=93690 BC), who was aware that the <A title=3D"Square root"=20
href=3D"http://en.wikipedia.org/wiki/Square_root">square roots</A> of =
certain=20
numbers such as 2 and 61 could not be exactly determined.<SUP =
class=3Dreference=20
id=3Dcite_ref-1><A=20
href=3D"http://en.wikipedia.org/wiki/Real_number#cite_note-1"><SPAN>[</SP=
AN>2<SPAN>]</SPAN></A></SUP>=20
Around 500 BC, the <A title=3D"Greek mathematics"=20
href=3D"http://en.wikipedia.org/wiki/Greek_mathematics">Greek =
mathematicians</A>=20
led by <A title=3DPythagoras=20
href=3D"http://en.wikipedia.org/wiki/Pythagoras">Pythagoras</A> realized =
the need=20
for irrational numbers, in particular the irrationality of the <A=20
title=3D"Square root of 2"=20
href=3D"http://en.wikipedia.org/wiki/Square_root_of_2">square root of =
2</A>.</P>
<P>The <A title=3D"Middle Ages"=20
href=3D"http://en.wikipedia.org/wiki/Middle_Ages">Middle Ages</A> saw =
the=20
acceptance of <A class=3Dmw-redirect title=3DZero=20
href=3D"http://en.wikipedia.org/wiki/Zero">zero</A>, <A=20
title=3D"Negative and non-negative numbers"=20
href=3D"http://en.wikipedia.org/wiki/Negative_and_non-negative_numbers">n=
egative</A>,=20
<A title=3DInteger =
href=3D"http://en.wikipedia.org/wiki/Integer">integral</A> and <A=20
title=3D"Fraction (mathematics)"=20
href=3D"http://en.wikipedia.org/wiki/Fraction_(mathematics)">fractional</=
A>=20
numbers, first by Indian and <A title=3D"Chinese mathematics"=20
href=3D"http://en.wikipedia.org/wiki/Chinese_mathematics">Chinese=20
mathematicians</A>, and then by <A title=3D"Mathematics in medieval =
Islam"=20
href=3D"http://en.wikipedia.org/wiki/Mathematics_in_medieval_Islam">Arabi=
c=20
mathematicians</A>, who were also the first to treat irrational numbers =
as=20
algebraic objects,<SUP class=3Dreference id=3Dcite_ref-2><A=20
href=3D"http://en.wikipedia.org/wiki/Real_number#cite_note-2"><SPAN>[</SP=
AN>3<SPAN>]</SPAN></A></SUP>=20
which was made possible by the development of <A title=3DAlgebra=20
href=3D"http://en.wikipedia.org/wiki/Algebra">algebra</A>. Arabic =
mathematicians=20
merged the concepts of "<A title=3DNumber=20
href=3D"http://en.wikipedia.org/wiki/Number">number</A>" and "<A=20
title=3D"Magnitude (mathematics)"=20
href=3D"http://en.wikipedia.org/wiki/Magnitude_(mathematics)">magnitude</=
A>" into=20
a more general idea of real numbers.<SUP class=3Dreference =
id=3Dcite_ref-3><A=20
href=3D"http://en.wikipedia.org/wiki/Real_number#cite_note-3"><SPAN>[</SP=
AN>4<SPAN>]</SPAN></A></SUP>=20
The <A title=3DEgypt =
href=3D"http://en.wikipedia.org/wiki/Egypt">Egyptian</A>=20
mathematician <A title=3D"Ab=C5=AB K=C4=81mil Shuj=C4=81 ibn Aslam"=20
href=3D"http://en.wikipedia.org/wiki/Ab%C5%AB_K%C4%81mil_Shuj%C4%81_ibn_A=
slam">Ab=C5=AB=20
K=C4=81mil Shuj=C4=81 ibn Aslam</A> (c. 850=E2=80=93930) was the first =
to accept irrational=20
numbers as solutions to <A title=3D"Quadratic equation"=20
href=3D"http://en.wikipedia.org/wiki/Quadratic_equation">quadratic =
equations</A>=20
or as <A title=3DCoefficient=20
href=3D"http://en.wikipedia.org/wiki/Coefficient">coefficients</A> in an =
<A=20
title=3DEquation =
href=3D"http://en.wikipedia.org/wiki/Equation">equation</A>, often=20
in the form of square roots, <A title=3D"Cube root"=20
href=3D"http://en.wikipedia.org/wiki/Cube_root">cube roots</A> and <A=20
title=3D"Nth root" href=3D"http://en.wikipedia.org/wiki/Nth_root">fourth =

roots</A>.<SUP class=3Dreference id=3Dcite_ref-4><A=20
href=3D"http://en.wikipedia.org/wiki/Real_number#cite_note-4"><SPAN>[</SP=
AN>5<SPAN>]</SPAN></A></SUP></P>
<P>In the 18th and 19th centuries there was much work on irrational and =
<A=20
title=3D"Transcendental number"=20
href=3D"http://en.wikipedia.org/wiki/Transcendental_number">transcendenta=
l=20
numbers</A>. <A title=3D"Johann Heinrich Lambert"=20
href=3D"http://en.wikipedia.org/wiki/Johann_Heinrich_Lambert">Lambert</A>=
 (1761)=20
gave the first flawed proof that =CF=80 cannot be rational; <A =
class=3Dmw-redirect=20
title=3DLegendre =
href=3D"http://en.wikipedia.org/wiki/Legendre">Legendre</A> (1794)=20
completed the proof, and showed that =CF=80 is not the square root of a =
rational=20
number. <A title=3D"Paolo Ruffini"=20
href=3D"http://en.wikipedia.org/wiki/Paolo_Ruffini">Ruffini</A> (1799) =
and <A=20
title=3D"Niels Henrik Abel"=20
href=3D"http://en.wikipedia.org/wiki/Niels_Henrik_Abel">Abel</A> (1842) =
both=20
constructed proofs of <A title=3D"Abel=E2=80=93Ruffini theorem"=20
href=3D"http://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem">Abel=E2=
=80=93Ruffini=20
theorem</A>: that the general <A title=3D"Quintic equation"=20
href=3D"http://en.wikipedia.org/wiki/Quintic_equation">quintic</A> or =
higher=20
equations cannot be solved by a general formula involving only =
arithmetical=20
operations and roots.</P>
<P><A title=3D"=C3=89variste Galois"=20
href=3D"http://en.wikipedia.org/wiki/%C3%89variste_Galois">=C3=89variste =
Galois</A>=20
(1832) developed techniques for determining whether a given equation =
could be=20
solved by radicals which gave rise to the field of <A title=3D"Galois =
theory"=20
href=3D"http://en.wikipedia.org/wiki/Galois_theory">Galois theory</A>. =
<A=20
title=3D"Joseph Liouville"=20
href=3D"http://en.wikipedia.org/wiki/Joseph_Liouville">Joseph =
Liouville</A> (1840)=20
showed that neither <I>e</I> nor <I>e</I><SUP>2</SUP> can be a root of =
an=20
integer <A title=3D"Quadratic equation"=20
href=3D"http://en.wikipedia.org/wiki/Quadratic_equation">quadratic =
equation</A>,=20
and then established existence of transcendental numbers, the proof =
being=20
subsequently displaced by Georg Cantor (1873). <A title=3D"Charles =
Hermite"=20
href=3D"http://en.wikipedia.org/wiki/Charles_Hermite">Charles =
Hermite</A> (1873)=20
first proved that <A title=3D"E (mathematical constant)"=20
href=3D"http://en.wikipedia.org/wiki/E_(mathematical_constant)"><I>e</I><=
/A> is=20
transcendental, and <A title=3D"Ferdinand von Lindemann"=20
href=3D"http://en.wikipedia.org/wiki/Ferdinand_von_Lindemann">Ferdinand =
von=20
Lindemann</A> (1882), showed that =CF=80 is transcendental. Lindemann's =
proof was=20
much simplified by Weierstrass (1885), still further by <A =
title=3D"David Hilbert"=20
href=3D"http://en.wikipedia.org/wiki/David_Hilbert">David Hilbert</A> =
(1893), and=20
has finally been made elementary by <A title=3D"Adolf Hurwitz"=20
href=3D"http://en.wikipedia.org/wiki/Adolf_Hurwitz">Hurwitz</A> and <A=20
title=3D"Paul Albert Gordan"=20
href=3D"http://en.wikipedia.org/wiki/Paul_Albert_Gordan">Paul Albert=20
Gordan</A>.</P>
<P>The development of <A title=3DCalculus=20
href=3D"http://en.wikipedia.org/wiki/Calculus">calculus</A> in the 1700s =
used the=20
entire set of real numbers without having defined them cleanly. The =
first=20
rigorous definition was given by <A title=3D"Georg Cantor"=20
href=3D"http://en.wikipedia.org/wiki/Georg_Cantor">Georg Cantor</A> in =
1871. In=20
1874 he showed that the set of all real numbers is <A =
class=3Dmw-redirect=20
title=3DUncountable =
href=3D"http://en.wikipedia.org/wiki/Uncountable">uncountably=20
infinite</A> but the set of all <A title=3D"Algebraic number"=20
href=3D"http://en.wikipedia.org/wiki/Algebraic_number">algebraic =
numbers</A> is <A=20
class=3Dmw-redirect title=3DCountable=20
href=3D"http://en.wikipedia.org/wiki/Countable">countably infinite</A>. =
Contrary=20
to widely held beliefs, his first method was not his famous <A=20
title=3D"Cantor's diagonal argument"=20
href=3D"http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument">diagon=
al=20
argument</A>, which he published in 1891. See <A=20
title=3D"Cantor's first uncountability proof"=20
href=3D"http://en.wikipedia.org/wiki/Cantor%27s_first_uncountability_proo=
f">Cantor's=20
first uncountability proof</A>.</P>
<P><A id=3DDefinition name=3DDefinition></A></P>
<H2><SPAN class=3Deditsection>[<A title=3D"Edit section: Definition"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D4">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>Definition</SPAN></H2>
<DIV class=3D"rellink relarticle mainarticle">Main article: <A=20
title=3D"Construction of the real numbers"=20
href=3D"http://en.wikipedia.org/wiki/Construction_of_the_real_numbers">Co=
nstruction=20
of the real numbers</A></DIV>
<P><A id=3DConstruction_from_the_rational_numbers=20
name=3DConstruction_from_the_rational_numbers></A></P>
<H3><SPAN class=3Deditsection>[<A=20
title=3D"Edit section: Construction from the rational numbers"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D5">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>Construction from the rational =
numbers</SPAN></H3>
<P>The real numbers can be constructed as a completion of the rational =
numbers=20
in such a way that a sequence defined by a decimal or binary expansion =
like {3,=20
3.1, 3.14, 3.141, 3.1415,...} <A class=3Dmw-redirect=20
title=3D"Convergence (mathematics)"=20
href=3D"http://en.wikipedia.org/wiki/Convergence_(mathematics)">converges=
</A> to a=20
unique real number. For details and other constructions of real numbers, =
see <A=20
title=3D"Construction of the real numbers"=20
href=3D"http://en.wikipedia.org/wiki/Construction_of_the_real_numbers">co=
nstruction=20
of the real numbers</A>.</P>
<P><A id=3DAxiomatic_approach name=3DAxiomatic_approach></A></P>
<H3><SPAN class=3Deditsection>[<A title=3D"Edit section: Axiomatic =
approach"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D6">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>Axiomatic approach</SPAN></H3>
<P>Let <B>R</B> denote the <A title=3D"Set (mathematics)"=20
href=3D"http://en.wikipedia.org/wiki/Set_(mathematics)">set</A> of all =
real=20
numbers. Then:</P>
<UL>
  <LI>The set <B>R</B> is a <A title=3D"Field (mathematics)"=20
  href=3D"http://en.wikipedia.org/wiki/Field_(mathematics)">field</A>, =
meaning=20
  that <A title=3DAddition=20
  href=3D"http://en.wikipedia.org/wiki/Addition">addition</A> and <A=20
  title=3DMultiplication=20
  =
href=3D"http://en.wikipedia.org/wiki/Multiplication">multiplication</A> =
are=20
  defined and have the usual properties.=20
  <LI>The field <B>R</B> is <A title=3D"Ordered field"=20
  href=3D"http://en.wikipedia.org/wiki/Ordered_field">ordered</A>, =
meaning that=20
  there is a <A title=3D"Total order"=20
  href=3D"http://en.wikipedia.org/wiki/Total_order">total order</A> =
=E2=89=A5 such that,=20
  for all real numbers <I>x</I>, <I>y</I> and <I>z</I>:=20
  <UL>
    <LI>if <I>x</I> =E2=89=A5 <I>y</I> then <I>x</I> + <I>z</I> =
=E2=89=A5 <I>y</I> + <I>z</I>;=20
    <LI>if <I>x</I> =E2=89=A5 0 and <I>y</I> =E2=89=A5 0 then <I>xy</I> =
=E2=89=A5 0. </LI></UL>
  <LI>The order is <A class=3Dmw-redirect title=3D"Dedekind completion"=20
  =
href=3D"http://en.wikipedia.org/wiki/Dedekind_completion">Dedekind-comple=
te</A>;=20
  that is, every <A title=3D"Empty set"=20
  href=3D"http://en.wikipedia.org/wiki/Empty_set">non-empty</A> subset =
<I>S</I> of=20
  <B>R</B> with an <A class=3Dmw-redirect title=3D"Upper bound"=20
  href=3D"http://en.wikipedia.org/wiki/Upper_bound">upper bound</A> in =
<B>R</B>=20
  has a <A title=3DSupremum =
href=3D"http://en.wikipedia.org/wiki/Supremum">least=20
  upper bound</A> (also called supremum) in <B>R</B>. </LI></UL>
<P>The last property is what differentiates the reals from the <A=20
title=3D"Rational number"=20
href=3D"http://en.wikipedia.org/wiki/Rational_number">rationals</A>. For =
example,=20
the set of rationals with square less than 2 has a rational upper bound =
(e.g.,=20
1.5) but no rational least upper bound, because the <A title=3D"Square =
root"=20
href=3D"http://en.wikipedia.org/wiki/Square_root">square root</A> of 2 =
is not=20
rational.</P>
<P>The real numbers are uniquely specified by the above properties. More =

precisely, given any two Dedekind-complete ordered fields =
<B>R</B><SUB>1</SUB>=20
and <B>R</B><SUB>2</SUB>, there exists a unique field <A =
title=3DIsomorphism=20
href=3D"http://en.wikipedia.org/wiki/Isomorphism">isomorphism</A> from=20
<B>R</B><SUB>1</SUB> to <B>R</B><SUB>2</SUB>, allowing us to think of =
them as=20
essentially the same mathematical object.</P>
<P>For another axiomatization of <B>R</B>, see <A=20
title=3D"Tarski's axiomatization of the reals"=20
href=3D"http://en.wikipedia.org/wiki/Tarski%27s_axiomatization_of_the_rea=
ls">Tarski's=20
axiomatization of the reals</A>.</P>
<P><A id=3DProperties name=3DProperties></A></P>
<H2><SPAN class=3Deditsection>[<A title=3D"Edit section: Properties"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D7">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>Properties</SPAN></H2>
<P><A id=3DCompleteness name=3DCompleteness></A></P>
<H3><SPAN class=3Deditsection>[<A title=3D"Edit section: Completeness"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D8">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>Completeness</SPAN></H3>
<P>The main reason for introducing the reals is that the reals contain =
all <A=20
title=3D"Limit (mathematics)"=20
href=3D"http://en.wikipedia.org/wiki/Limit_(mathematics)">limits</A>. =
More=20
technically, the reals are <A class=3Dmw-redirect title=3D"Completeness =
(topology)"=20
href=3D"http://en.wikipedia.org/wiki/Completeness_(topology)">complete</A=
> (in the=20
sense of <A title=3D"Metric space"=20
href=3D"http://en.wikipedia.org/wiki/Metric_space">metric spaces</A> or =
<A=20
title=3D"Uniform space" =
href=3D"http://en.wikipedia.org/wiki/Uniform_space">uniform=20
spaces</A>, which is a different sense than the Dedekind completeness of =
the=20
order in the previous section). This means the following:</P>
<P>A <A title=3DSequence =
href=3D"http://en.wikipedia.org/wiki/Sequence">sequence</A>=20
(<I>x</I><SUB><I>n</I></SUB>) of real numbers is called a <I><A=20
title=3D"Cauchy sequence"=20
href=3D"http://en.wikipedia.org/wiki/Cauchy_sequence">Cauchy =
sequence</A></I> if=20
for any =CE=B5&nbsp;&gt;&nbsp;0 there exists an integer <I>N</I> =
(possibly depending=20
on =CE=B5) such that the <A title=3DDistance=20
href=3D"http://en.wikipedia.org/wiki/Distance">distance</A>=20
|<I>x</I><SUB><I>n</I></SUB>&nbsp;=E2=88=92&nbsp;<I>x</I><SUB><I>m</I></S=
UB>| is less=20
than =CE=B5 for all <I>n</I> and <I>m</I> that are both greater than =
<I>N</I>. In=20
other words, a sequence is a <A class=3Dmw-redirect title=3D"Augustin =
Louis Cauchy"=20
href=3D"http://en.wikipedia.org/wiki/Augustin_Louis_Cauchy">Cauchy</A> =
sequence if=20
its elements <I>x</I><SUB><I>n</I></SUB> eventually come and remain =
arbitrarily=20
close to each other.</P>
<P>A sequence (<I>x</I><SUB><I>n</I></SUB>) <I>converges to the =
limit</I>=20
<I>x</I> if for any =CE=B5&nbsp;&gt;&nbsp;0 there exists an integer =
<I>N</I>=20
(possibly depending on =CE=B5) such that the distance=20
|<I>x</I><SUB><I>n</I></SUB>&nbsp;=E2=88=92&nbsp;<I>x</I>| is less than =
=CE=B5 provided that=20
<I>n</I> is greater than <I>N</I>. In other words, a sequence has limit =
<I>x</I>=20
if its elements eventually come and remain arbitrarily close to =
<I>x</I>.</P>
<P>It is easy to see that every convergent sequence is a Cauchy =
sequence. An=20
important fact about the real numbers is that the converse is also =
true:</P>
<DL>
  <DD><B>Every Cauchy sequence of real numbers is convergent.</B> =
</DD></DL>
<P>That is, the reals are complete.</P>
<P>Note that the rationals are not complete. For example, the sequence =
(1, 1.4,=20
1.41, 1.414, 1.4142, 1.41421, ...) is Cauchy but it does not converge to =
a=20
rational number. (In the real numbers, in contrast, it converges to the =
<A=20
title=3D"Square root" =
href=3D"http://en.wikipedia.org/wiki/Square_root">square=20
root</A> of 2.)</P>
<P>The existence of limits of Cauchy sequences is what makes <A =
title=3DCalculus=20
href=3D"http://en.wikipedia.org/wiki/Calculus">calculus</A> work and is =
of great=20
practical use. The standard numerical test to determine if a sequence =
has a=20
limit is to test if it is a Cauchy sequence, as the limit is typically =
not known=20
in advance.</P>
<P>For example, the standard series of the <A title=3D"Exponential =
function"=20
href=3D"http://en.wikipedia.org/wiki/Exponential_function">exponential=20
function</A></P>
<DL>
  <DD><IMG class=3Dtex alt=3D"\mathrm{e}^x =3D \sum_{n=3D0}^{\infty} =
\frac{x^n}{n!}"=20
  =
src=3D"http://upload.wikimedia.org/math/7/4/f/74fefb1e2fc4c152e1157cb7780=
bab79.png">=20
  </DD></DL>
<P>converges to a real number because for every <I>x</I> the sums</P>
<DL>
  <DD><IMG class=3Dtex alt=3D"\sum_{n=3DN}^{M} \frac{x^n}{n!}"=20
  =
src=3D"http://upload.wikimedia.org/math/b/3/3/b33758377a345927bd1dde05dcf=
6c63a.png">=20
  </DD></DL>
<P>can be made arbitrarily small by choosing <I>N</I> sufficiently =
large. This=20
proves that the sequence is Cauchy, so we know that the sequence =
converges even=20
if the limit is not known in advance.</P>
<P><A id=3D.22The_complete_ordered_field.22=20
name=3D.22The_complete_ordered_field.22></A></P>
<H3><SPAN class=3Deditsection>[<A=20
title=3D'Edit section: "The complete ordered field"'=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D9">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>"The complete ordered field"</SPAN></H3>
<P>The real numbers are often described as "the complete ordered field", =
a=20
phrase that can be interpreted in several ways.</P>
<P>First, an order can be <A title=3D"Complete lattice"=20
href=3D"http://en.wikipedia.org/wiki/Complete_lattice">lattice-complete</=
A>. It is=20
easy to see that no ordered field can be lattice-complete, because it =
can have=20
no largest element (given any element <I>z</I>, <I>z</I>&nbsp;+&nbsp;1 =
is=20
larger), so this is not the sense that is meant.</P>
<P>Additionally, an order can be <A class=3Dmw-redirect=20
title=3D"Dedekind completion"=20
href=3D"http://en.wikipedia.org/wiki/Dedekind_completion">Dedekind-comple=
te</A>,=20
as defined in the section <B>Axioms</B>. The uniqueness result at the =
end of=20
that section justifies using the word "the" in the phrase "complete =
ordered=20
field" when this is the sense of "complete" that is meant. This sense of =

completeness is most closely related to the construction of the reals =
from=20
Dedekind cuts, since that construction starts from an ordered field (the =

rationals) and then forms the Dedekind-completion of it in a standard =
way.</P>
<P>These two notions of completeness ignore the field structure. =
However, an <A=20
class=3Dmw-redirect title=3D"Ordered group"=20
href=3D"http://en.wikipedia.org/wiki/Ordered_group">ordered group</A> =
(in this=20
case, the additive group of the field) defines a <A title=3D"Uniform =
space"=20
href=3D"http://en.wikipedia.org/wiki/Uniform_space">uniform</A> =
structure, and=20
uniform structures have a notion of <A class=3Dmw-redirect=20
title=3D"Completeness (topology)"=20
href=3D"http://en.wikipedia.org/wiki/Completeness_(topology)">completenes=
s=20
(topology)</A>; the description in the section <B>Completeness</B> above =
is a=20
special case. (We refer to the notion of completeness in uniform spaces =
rather=20
than the related and better known notion for <A title=3D"Metric space"=20
href=3D"http://en.wikipedia.org/wiki/Metric_space">metric spaces</A>, =
since the=20
definition of metric space relies on already having a characterisation =
of the=20
real numbers.) It is not true that <B>R</B> is the <I>only</I> uniformly =

complete ordered field, but it is the only uniformly complete <I><A=20
title=3D"Archimedean field"=20
href=3D"http://en.wikipedia.org/wiki/Archimedean_field">Archimedean =
field</A></I>,=20
and indeed one often hears the phrase "complete Archimedean field" =
instead of=20
"complete ordered field". Since it can be proved that any uniformly =
complete=20
Archimedean field must also be Dedekind-complete (and vice versa, of =
course),=20
this justifies using "the" in the phrase "the complete Archimedean =
field". This=20
sense of completeness is most closely related to the construction of the =
reals=20
from Cauchy sequences (the construction carried out in full in this =
article),=20
since it starts with an Archimedean field (the rationals) and forms the =
uniform=20
completion of it in a standard way.</P>
<P>But the original use of the phrase "complete Archimedean field" was =
by <A=20
title=3D"David Hilbert" =
href=3D"http://en.wikipedia.org/wiki/David_Hilbert">David=20
Hilbert</A>, who meant still something else by it. He meant that the =
real=20
numbers form the <I>largest</I> Archimedean field in the sense that =
every other=20
Archimedean field is a subfield of <B>R</B>. Thus <B>R</B> is "complete" =
in the=20
sense that nothing further can be added to it without making it no =
longer an=20
Archimedean field. This sense of completeness is most closely related to =
the=20
construction of the reals from <A title=3D"Surreal number"=20
href=3D"http://en.wikipedia.org/wiki/Surreal_number">surreal =
numbers</A>, since=20
that construction starts with a proper class that contains every ordered =
field=20
(the surreals) and then selects from it the largest Archimedean =
subfield.</P>
<P><A id=3DAdvanced_properties name=3DAdvanced_properties></A></P>
<H3><SPAN class=3Deditsection>[<A title=3D"Edit section: Advanced =
properties"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D10">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>Advanced properties</SPAN></H3>
<P>The reals are <A class=3Dmw-redirect title=3DUncountable=20
href=3D"http://en.wikipedia.org/wiki/Uncountable">uncountable</A>; that =
is, there=20
are strictly more real numbers than <A title=3D"Natural number"=20
href=3D"http://en.wikipedia.org/wiki/Natural_number">natural =
numbers</A>, even=20
though both sets are <A title=3D"Infinite set"=20
href=3D"http://en.wikipedia.org/wiki/Infinite_set">infinite</A>. In =
fact, the <A=20
title=3D"Cardinality of the continuum"=20
href=3D"http://en.wikipedia.org/wiki/Cardinality_of_the_continuum">cardin=
ality of=20
the reals</A> equals that of the set of subsets (i.e., the power set) of =
the=20
natural numbers, and <A title=3D"Cantor's diagonal argument"=20
href=3D"http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument">Cantor=
's=20
diagonal argument</A> states that the latter set's cardinality is =
strictly=20
bigger than the cardinality of <B>N</B>. Since only a countable set of =
real=20
numbers can be <A title=3D"Algebraic number"=20
href=3D"http://en.wikipedia.org/wiki/Algebraic_number">algebraic</A>, <A =

title=3D"Almost all" =
href=3D"http://en.wikipedia.org/wiki/Almost_all">almost all</A>=20
real numbers are <A title=3D"Transcendental number"=20
href=3D"http://en.wikipedia.org/wiki/Transcendental_number">transcendenta=
l</A>.=20
The non-existence of a subset of the reals with cardinality strictly =
between=20
that of the integers and the reals is known as the <A=20
title=3D"Continuum hypothesis"=20
href=3D"http://en.wikipedia.org/wiki/Continuum_hypothesis">continuum=20
hypothesis</A>. The continuum hypothesis can neither be proved nor be =
disproved;=20
it is <A class=3Dmw-redirect title=3D"Logical independence"=20
href=3D"http://en.wikipedia.org/wiki/Logical_independence">independent</A=
> from=20
the <A class=3Dmw-redirect title=3D"Axiomatic set theory"=20
href=3D"http://en.wikipedia.org/wiki/Axiomatic_set_theory">axioms of set =

theory</A>.</P>
<P>The real numbers form a <A title=3D"Metric space"=20
href=3D"http://en.wikipedia.org/wiki/Metric_space">metric space</A>: the =
distance=20
between <I>x</I> and <I>y</I> is defined to be the <A title=3D"Absolute =
value"=20
href=3D"http://en.wikipedia.org/wiki/Absolute_value">absolute value</A>=20
|<I>x</I>&nbsp;=E2=88=92&nbsp;<I>y</I>|. By virtue of being a <A =
title=3D"Total order"=20
href=3D"http://en.wikipedia.org/wiki/Total_order">totally ordered</A> =
set, they=20
also carry an <A title=3D"Order topology"=20
href=3D"http://en.wikipedia.org/wiki/Order_topology">order topology</A>; =
the <A=20
title=3DTopology =
href=3D"http://en.wikipedia.org/wiki/Topology">topology</A> arising=20
from the metric and the one arising from the order are identical. The =
reals are=20
a <A class=3Dmw-redirect title=3DContractible=20
href=3D"http://en.wikipedia.org/wiki/Contractible">contractible</A> =
(hence <A=20
title=3D"Connected space"=20
href=3D"http://en.wikipedia.org/wiki/Connected_space">connected</A> and =
<A=20
class=3Dmw-redirect title=3D"Simply connected"=20
href=3D"http://en.wikipedia.org/wiki/Simply_connected">simply =
connected</A>), <A=20
title=3D"Separable space"=20
href=3D"http://en.wikipedia.org/wiki/Separable_space">separable</A> =
metric space=20
of <A title=3DDimension=20
href=3D"http://en.wikipedia.org/wiki/Dimension">dimension</A> 1, and are =
<A=20
class=3Dmw-redirect title=3D"First category"=20
href=3D"http://en.wikipedia.org/wiki/First_category">everywhere =
dense</A>. The=20
real numbers are <A class=3Dmw-redirect title=3D"Local compactness"=20
href=3D"http://en.wikipedia.org/wiki/Local_compactness">locally =
compact</A> but=20
not <A title=3D"Compact space"=20
href=3D"http://en.wikipedia.org/wiki/Compact_space">compact</A>. There =
are various=20
properties that uniquely specify them; for instance, all unbounded, =
connected,=20
and separable <A title=3D"Total order"=20
href=3D"http://en.wikipedia.org/wiki/Total_order">order topologies</A> =
are=20
necessarily <A class=3Dmw-redirect title=3DHomeomorphic=20
href=3D"http://en.wikipedia.org/wiki/Homeomorphic">homeomorphic</A> to =
the=20
reals.</P>
<P>Every nonnegative real number has a <A title=3D"Square root"=20
href=3D"http://en.wikipedia.org/wiki/Square_root">square root</A> in =
<B>R</B>, and=20
no negative number does. This shows that the order on <B>R</B> is =
determined by=20
its algebraic structure. Also, every polynomial of odd degree admits at =
least=20
one real root: these two properties make <B>R</B> the premier example of =
a <A=20
title=3D"Real closed field"=20
href=3D"http://en.wikipedia.org/wiki/Real_closed_field">real closed =
field</A>.=20
Proving this is the first half of one proof of the <A=20
title=3D"Fundamental theorem of algebra"=20
href=3D"http://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra">fund=
amental=20
theorem of algebra</A>.</P>
<P>The reals carry a canonical <A title=3D"Measure (mathematics)"=20
href=3D"http://en.wikipedia.org/wiki/Measure_(mathematics)">measure</A>, =
the <A=20
title=3D"Lebesgue measure"=20
href=3D"http://en.wikipedia.org/wiki/Lebesgue_measure">Lebesgue =
measure</A>, which=20
is the <A title=3D"Haar measure"=20
href=3D"http://en.wikipedia.org/wiki/Haar_measure">Haar measure</A> on =
their=20
structure as a <A title=3D"Topological group"=20
href=3D"http://en.wikipedia.org/wiki/Topological_group">topological =
group</A>=20
normalised such that the <A title=3D"Unit interval"=20
href=3D"http://en.wikipedia.org/wiki/Unit_interval">unit interval</A> =
[0,1] has=20
measure 1.</P>
<P>The supremum axiom of the reals refers to subsets of the reals and is =

therefore a second-order logical statement. It is not possible to =
characterize=20
the reals with <A title=3D"First-order logic"=20
href=3D"http://en.wikipedia.org/wiki/First-order_logic">first-order =
logic</A>=20
alone: the <A class=3Dmw-redirect title=3D"L=C3=B6wenheim-Skolem =
theorem"=20
href=3D"http://en.wikipedia.org/wiki/L%C3%B6wenheim-Skolem_theorem">L=C3=B6=
wenheim-Skolem=20
theorem</A> implies that there exists a countable dense subset of the =
real=20
numbers satisfying exactly the same sentences in first order logic as =
the real=20
numbers themselves. The set of <A title=3D"Hyperreal number"=20
href=3D"http://en.wikipedia.org/wiki/Hyperreal_number">hyperreal =
numbers</A>=20
satisfies the same first order sentences as <B>R</B>. Ordered fields =
that=20
satisfy the same first-order sentences as <B>R</B> are called <A=20
title=3D"Non-standard model"=20
href=3D"http://en.wikipedia.org/wiki/Non-standard_model">nonstandard =
models</A> of=20
<B>R</B>. This is what makes <A title=3D"Non-standard analysis"=20
href=3D"http://en.wikipedia.org/wiki/Non-standard_analysis">nonstandard=20
analysis</A> work; by proving a first-order statement in some =
nonstandard model=20
(which may be easier than proving it in <B>R</B>), we know that the same =

statement must also be true of <B>R</B>.</P>
<P><A id=3DGeneralizations_and_extensions=20
name=3DGeneralizations_and_extensions></A></P>
<H2><SPAN class=3Deditsection>[<A=20
title=3D"Edit section: Generalizations and extensions"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D11">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>Generalizations and extensions</SPAN></H2>
<P>The real numbers can be generalized and extended in several different =

directions:</P>
<UL>
  <LI>The <A title=3D"Complex number"=20
  href=3D"http://en.wikipedia.org/wiki/Complex_number">complex =
numbers</A> contain=20
  solutions to all <A title=3DPolynomial=20
  href=3D"http://en.wikipedia.org/wiki/Polynomial">polynomial</A> =
equations and=20
  hence are an <A title=3D"Algebraically closed field"=20
  =
href=3D"http://en.wikipedia.org/wiki/Algebraically_closed_field">algebrai=
cally=20
  closed field</A> unlike the real numbers. However, the complex numbers =
are not=20
  an <A title=3D"Ordered field"=20
  href=3D"http://en.wikipedia.org/wiki/Ordered_field">ordered field</A>. =

  <LI>The <A class=3Dmw-redirect title=3D"Affinely extended real number =
system"=20
  =
href=3D"http://en.wikipedia.org/wiki/Affinely_extended_real_number_system=
">affinely=20
  extended real number system</A> adds two elements +=E2=88=9E and =
=E2=88=92=E2=88=9E. It is a <A=20
  title=3D"Compact space"=20
  href=3D"http://en.wikipedia.org/wiki/Compact_space">compact space</A>. =
It is no=20
  longer a field, not even an additive group; it still has a <A=20
  title=3D"Total order" =
href=3D"http://en.wikipedia.org/wiki/Total_order">total=20
  order</A>; moreover, it is a <A title=3D"Complete lattice"=20
  href=3D"http://en.wikipedia.org/wiki/Complete_lattice">complete =
lattice</A>.=20
  <LI>The <A title=3D"Real projective line"=20
  href=3D"http://en.wikipedia.org/wiki/Real_projective_line">real =
projective=20
  line</A> adds only one value =E2=88=9E. It is also a compact space. =
Again, it is no=20
  longer a field, not even an additive group. However, it allows =
division of a=20
  non-zero element by zero. It is not ordered anymore.=20
  <LI>The <A title=3D"Long line (topology)"=20
  href=3D"http://en.wikipedia.org/wiki/Long_line_(topology)">long real =
line</A>=20
  pastes together =E2=84=B5<SUB>1</SUB>* + =E2=84=B5<SUB>1</SUB> copies =
of the real line plus a=20
  single point (here =E2=84=B5<SUB>1</SUB>* denotes the reversed =
ordering of=20
  =E2=84=B5<SUB>1</SUB>) to create an ordered set that is "locally" =
identical to the=20
  real numbers, but somehow longer; for instance, there is an =
order-preserving=20
  embedding of =E2=84=B5<SUB>1</SUB> in the long real line but not in =
the real numbers.=20
  The long real line is the largest ordered set that is complete and =
locally=20
  Archimedean. As with the previous two examples, this set is no longer =
a field=20
  or additive group.=20
  <LI>Ordered fields extending the reals are the <A title=3D"Hyperreal =
number"=20
  href=3D"http://en.wikipedia.org/wiki/Hyperreal_number">hyperreal =
numbers</A> and=20
  the <A title=3D"Surreal number"=20
  href=3D"http://en.wikipedia.org/wiki/Surreal_number">surreal =
numbers</A>; both=20
  of them contain <A title=3DInfinitesimal=20
  href=3D"http://en.wikipedia.org/wiki/Infinitesimal">infinitesimal</A> =
and=20
  infinitely large numbers and thus are not <A title=3D"Archimedean =
group"=20
  =
href=3D"http://en.wikipedia.org/wiki/Archimedean_group">Archimedean</A>. =

  <LI><A title=3DHermitian=20
  href=3D"http://en.wikipedia.org/wiki/Hermitian">Self-adjoint =
operators</A> on a=20
  <A title=3D"Hilbert space"=20
  href=3D"http://en.wikipedia.org/wiki/Hilbert_space">Hilbert space</A> =
(for=20
  example, self-adjoint square complex <A class=3Dmw-redirect=20
  title=3D"Matrix (math)"=20
  href=3D"http://en.wikipedia.org/wiki/Matrix_(math)">matrices</A>) =
generalize the=20
  reals in many respects: they can be ordered (though not totally =
ordered), they=20
  are complete, all their <A class=3Dmw-redirect title=3DEigenvector=20
  href=3D"http://en.wikipedia.org/wiki/Eigenvector">eigenvalues</A> are =
real and=20
  they form a real <A title=3D"Associative algebra"=20
  href=3D"http://en.wikipedia.org/wiki/Associative_algebra">associative=20
  algebra</A>. <A class=3Dmw-redirect title=3DPositive-definite=20
  =
href=3D"http://en.wikipedia.org/wiki/Positive-definite">Positive-definite=
</A>=20
  operators correspond to the positive reals and <A title=3D"Normal =
operator"=20
  href=3D"http://en.wikipedia.org/wiki/Normal_operator">normal =
operators</A>=20
  correspond to the complex numbers. </LI></UL>
<P><A id=3D.22Reals.22_in_set_theory =
name=3D.22Reals.22_in_set_theory></A></P>
<H2><SPAN class=3Deditsection>[<A title=3D'Edit section: "Reals" in set =
theory'=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D12">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>"Reals" in set theory</SPAN></H2>
<P>In <A title=3D"Set theory" =
href=3D"http://en.wikipedia.org/wiki/Set_theory">set=20
theory</A>, specifically <A title=3D"Descriptive set theory"=20
href=3D"http://en.wikipedia.org/wiki/Descriptive_set_theory">descriptive =
set=20
theory</A> the <A title=3D"Baire space (set theory)"=20
href=3D"http://en.wikipedia.org/wiki/Baire_space_(set_theory)">Baire =
space</A> is=20
used as a surrogate for the real numbers since the latter have some =
topological=20
properties (connectedness) that are a technical inconvenience. Elements =
of Baire=20
space are referred to as "reals".</P>
<P><A id=3DSee_also name=3DSee_also></A></P>
<H2><SPAN class=3Deditsection>[<A title=3D"Edit section: See also"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D13">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>See also</SPAN></H2>
<DIV style=3D"-moz-column-count: 2; column-count: 2; =
-webkit-column-count: 2">
<UL>
  <LI><A title=3DCompleteness=20
  =
href=3D"http://en.wikipedia.org/wiki/Completeness#Mathematical_completene=
ss">Completeness</A>=20

  <LI><A title=3D"Continued fraction"=20
  href=3D"http://en.wikipedia.org/wiki/Continued_fraction">Continued =
fraction</A>=20
  <LI><A title=3D"Limit of a sequence"=20
  href=3D"http://en.wikipedia.org/wiki/Limit_of_a_sequence">Limit of a=20
  sequence</A>=20
  <LI><A title=3D"Real analysis"=20
  href=3D"http://en.wikipedia.org/wiki/Real_analysis">Real analysis</A>=20
  <LI><A title=3D"Simon Stevin"=20
  href=3D"http://en.wikipedia.org/wiki/Simon_Stevin">Simon Stevin</A>=20
  <LI><A title=3D"Imaginary number"=20
  href=3D"http://en.wikipedia.org/wiki/Imaginary_number">Imaginary =
number</A>=20
  <LI><A title=3D"Complex number"=20
  href=3D"http://en.wikipedia.org/wiki/Complex_number">Complex =
number</A>=20
</LI></UL></DIV>
<P><A id=3DNotes name=3DNotes></A></P>
<H2><SPAN class=3Deditsection>[<A title=3D"Edit section: Notes"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D14">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>Notes</SPAN></H2>
<DIV class=3Dreferences-small>
<OL class=3Dreferences>
  <LI id=3Dcite_note-0><B><A=20
  href=3D"http://en.wikipedia.org/wiki/Real_number#cite_ref-0">^</A></B> =
<A=20
  title=3D"Scott Aaronson"=20
  href=3D"http://en.wikipedia.org/wiki/Scott_Aaronson">Scott =
Aaronson</A>, <I><A=20
  class=3D"external text" title=3Dhttp://arxiv.org/abs/quant-ph/0502072=20
  href=3D"http://arxiv.org/abs/quant-ph/0502072" =
rel=3Dnofollow>NP-complete Problems=20
  and Physical Reality</A></I>, ACM <A class=3Dmw-redirect =
title=3DSIGACT=20
  href=3D"http://en.wikipedia.org/wiki/SIGACT">SIGACT</A> News, Vol. 36, =
No. 1.=20
  (March 2005), pp. 30-52.=20
  <LI id=3Dcite_note-1><B><A=20
  href=3D"http://en.wikipedia.org/wiki/Real_number#cite_ref-1">^</A></B> =
T. K.=20
  Puttaswamy, "The Accomplishments of Ancient Indian Mathematicians", =
pp. 410=E2=80=931,=20
  in <SPAN class=3Dcitation id=3DCITEREFSelinD.27Ambrosio2000>Selin, =
Helaine;=20
  D'Ambrosio, Ubiratan (2000), <I><SPAN>Mathematics Across Cultures: The =
History=20
  of Non-western Mathematics</SPAN></I>, <A=20
  title=3D"Springer Science+Business Media"=20
  =
href=3D"http://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media">S=
pringer</A>,=20
  <A class=3Dinternal=20
  =
href=3D"http://en.wikipedia.org/wiki/Special:BookSources/1402002602">ISBN=
=20
  1402002602</A></SPAN><SPAN class=3DZ3988=20
  =
title=3Dctx_ver=3DZ39.88-2004&amp;rft_val_fmt=3Dinfo%3Aofi%2Ffmt%3Akev%3A=
mtx%3Abook&amp;rft.genre=3Dbook&amp;rft.btitle=3DMathematics+Across+Cultu=
res%3A+The+History+of+Non-western+Mathematics&amp;rft.aulast=3DSelin&amp;=
rft.aufirst=3DHelaine&amp;rft.au=3DSelin%2C+Helaine&amp;rft.au=3DD%27Ambr=
osio%2C+Ubiratan&amp;rft.date=3D2000&amp;rft.pub=3D%5B%5BSpringer+Science=
%2BBusiness+Media%7CSpringer%5D%5D&amp;rft.isbn=3D1402002602&amp;rfr_id=3D=
info:sid/en.wikipedia.org:Real_number><SPAN=20
  style=3D"DISPLAY: none">&nbsp;</SPAN></SPAN>=20
  <LI id=3Dcite_note-2><B><A=20
  href=3D"http://en.wikipedia.org/wiki/Real_number#cite_ref-2">^</A></B> =
<SPAN=20
  class=3Dcitation id=3DCITEREFO.27ConnorRobertson><A =
class=3Dmw-redirect=20
  title=3D"John J. O'Connor (mathematician)"=20
  =
href=3D"http://en.wikipedia.org/wiki/John_J._O%27Connor_(mathematician)">=
O'Connor,=20
  John J.</A>; <A title=3D"Edmund F. Robertson"=20
  href=3D"http://en.wikipedia.org/wiki/Edmund_F._Robertson">Robertson, =
Edmund=20
  F.</A>, "<A class=3D"external text"=20
  =
title=3Dhttp://www-history.mcs.st-andrews.ac.uk/HistTopics/Arabic_mathema=
tics.html=20
  =
href=3D"http://www-history.mcs.st-andrews.ac.uk/HistTopics/Arabic_mathema=
tics.html"=20
  rel=3Dnofollow>Arabic mathematics: forgotten brilliance?</A>", =
<I><SPAN><A=20
  title=3D"MacTutor History of Mathematics archive"=20
  =
href=3D"http://en.wikipedia.org/wiki/MacTutor_History_of_Mathematics_arch=
ive">MacTutor=20
  History of Mathematics archive</A></SPAN></I></SPAN><SPAN =
class=3DZ3988=20
  =
title=3Dctx_ver=3DZ39.88-2004&amp;rft_val_fmt=3Dinfo%3Aofi%2Ffmt%3Akev%3A=
mtx%3Abook&amp;rft.genre=3Dbookitem&amp;rft.btitle=3DArabic+mathematics%3=
A+forgotten+brilliance%3F&amp;rft.atitle=3D%5B%5BMacTutor+History+of+Math=
ematics+archive%5D%5D&amp;rft.aulast=3DO%27Connor&amp;rft.aufirst=3DJohn+=
J.&amp;rft.au=3DO%27Connor%2C+John+J.&amp;rft.au=3DRobertson%2C+Edmund+F.=
&amp;rfr_id=3Dinfo:sid/en.wikipedia.org:Real_number><SPAN=20
  style=3D"DISPLAY: none">&nbsp;</SPAN></SPAN>.=20
  <LI id=3Dcite_note-3><B><A=20
  href=3D"http://en.wikipedia.org/wiki/Real_number#cite_ref-3">^</A></B> =
<SPAN=20
  class=3Dcitation id=3DCITEREFMatvievskaya1987>Matvievskaya, Galina =
(1987), "The=20
  Theory of Quadratic Irrationals in Medieval Oriental Mathematics", =
<I><A=20
  title=3D"New York Academy of Sciences"=20
  =
href=3D"http://en.wikipedia.org/wiki/New_York_Academy_of_Sciences">Annals=
 of the=20
  New York Academy of Sciences</A></I> <B>500</B>: 253-277 [254], <A=20
  title=3D"Digital object identifier"=20
  =
href=3D"http://en.wikipedia.org/wiki/Digital_object_identifier">doi</A>:<=
SPAN=20
  class=3Dneverexpand><A class=3D"external text"=20
  title=3Dhttp://dx.doi.org/10.1111%2Fj.1749-6632.1987.tb37206.x=20
  href=3D"http://dx.doi.org/10.1111%2Fj.1749-6632.1987.tb37206.x"=20
  =
rel=3Dnofollow>10.1111/j.1749-6632.1987.tb37206.x</A></SPAN></SPAN><SPAN =

  class=3DZ3988=20
  =
title=3Dctx_ver=3DZ39.88-2004&amp;rft_val_fmt=3Dinfo%3Aofi%2Ffmt%3Akev%3A=
mtx%3Ajournal&amp;rft.genre=3Darticle&amp;rft.atitle=3DThe+Theory+of+Quad=
ratic+Irrationals+in+Medieval+Oriental+Mathematics&amp;rft.jtitle=3D%5B%5=
BNew+York+Academy+of+Sciences%7CAnnals+of+the+New+York+Academy+of+Science=
s%5D%5D&amp;rft.aulast=3DMatvievskaya&amp;rft.aufirst=3DGalina&amp;rft.au=
=3DMatvievskaya%2C+Galina&amp;rft.date=3D1987&amp;rft.volume=3D500&amp;rf=
t.pages=3D253-277+%5B254%5D&amp;rft_id=3Dinfo:doi/10.1111%2Fj.1749-6632.1=
987.tb37206.x&amp;rfr_id=3Dinfo:sid/en.wikipedia.org:Real_number><SPAN=20
  style=3D"DISPLAY: none">&nbsp;</SPAN></SPAN>=20
  <LI id=3Dcite_note-4><B><A=20
  href=3D"http://en.wikipedia.org/wiki/Real_number#cite_ref-4">^</A></B> =
Jacques=20
  Sesiano, "Islamic mathematics", p. 148, in <SPAN class=3Dcitation=20
  id=3DCITEREFSelinD.27Ambrosio2000>Selin, Helaine; D'Ambrosio, Ubiratan =
(2000),=20
  <I><SPAN>Mathematics Across Cultures: The History of Non-western=20
  Mathematics</SPAN></I>, <A title=3D"Springer Science+Business Media"=20
  =
href=3D"http://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media">S=
pringer</A>,=20
  <A class=3Dinternal=20
  =
href=3D"http://en.wikipedia.org/wiki/Special:BookSources/1402002602">ISBN=
=20
  1402002602</A></SPAN><SPAN class=3DZ3988=20
  =
title=3Dctx_ver=3DZ39.88-2004&amp;rft_val_fmt=3Dinfo%3Aofi%2Ffmt%3Akev%3A=
mtx%3Abook&amp;rft.genre=3Dbook&amp;rft.btitle=3DMathematics+Across+Cultu=
res%3A+The+History+of+Non-western+Mathematics&amp;rft.aulast=3DSelin&amp;=
rft.aufirst=3DHelaine&amp;rft.au=3DSelin%2C+Helaine&amp;rft.au=3DD%27Ambr=
osio%2C+Ubiratan&amp;rft.date=3D2000&amp;rft.pub=3D%5B%5BSpringer+Science=
%2BBusiness+Media%7CSpringer%5D%5D&amp;rft.isbn=3D1402002602&amp;rfr_id=3D=
info:sid/en.wikipedia.org:Real_number><SPAN=20
  style=3D"DISPLAY: none">&nbsp;</SPAN></SPAN> </LI></OL></DIV>
<P><A id=3DReferences name=3DReferences></A></P>
<H2><SPAN class=3Deditsection>[<A title=3D"Edit section: References"=20
href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D15">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>References</SPAN></H2>
<UL>
  <LI><A title=3D"Georg Cantor"=20
  href=3D"http://en.wikipedia.org/wiki/Georg_Cantor">Georg Cantor</A>, =
1874, "=C3=9Cber=20
  eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen",=20
  <I>Journal f=C3=BCr die Reine und Angewandte Mathematik</I>, volume =
77, pages=20
  258-262.=20
  <LI>Robert Katz, 1964, <I>Axiomatic Analysis</I>, D. C. Heath and =
Company.=20
  <LI><A title=3D"Edmund Landau"=20
  href=3D"http://en.wikipedia.org/wiki/Edmund_Landau">Edmund Landau</A>, =
2001, <A=20
  class=3Dinternal=20
  =
href=3D"http://en.wikipedia.org/wiki/Special:BookSources/082182693X">ISBN=
=20
  0-8218-2693-X</A>, <I>Foundations of Analysis</I>, <A=20
  title=3D"American Mathematical Society"=20
  =
href=3D"http://en.wikipedia.org/wiki/American_Mathematical_Society">Ameri=
can=20
  Mathematical Society</A>.=20
  <LI>Howie, John M., <I>Real Analysis</I>, Springer, 2005, <A =
class=3Dinternal=20
  =
href=3D"http://en.wikipedia.org/wiki/Special:BookSources/1852333146">ISBN=
=20
  1-85233-314-6</A> </LI></UL>
<P><A id=3DExternal_links name=3DExternal_links></A></P>
<H2><SPAN class=3Deditsection>[<A title=3D"Edit section: External links" =

href=3D"http://en.wikipedia.org/w/index.php?title=3DReal_number&amp;actio=
n=3Dedit&amp;section=3D16">edit</A>]</SPAN>=20
<SPAN class=3Dmw-headline>External links</SPAN></H2>
<UL>
  <LI><A class=3D"external text"=20
  =
title=3Dhttp://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Real_numbe=
rs_1.html=20
  =
href=3D"http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Real_numbe=
rs_1.html"=20
  rel=3Dnofollow>The real numbers: Pythagoras to Stevin</A>=20
  <LI><A class=3D"external text"=20
  =
title=3Dhttp://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Real_numbe=
rs_2.html=20
  =
href=3D"http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Real_numbe=
rs_2.html"=20
  rel=3Dnofollow>The real numbers: Stevin to Hilbert</A>=20
  <LI><A class=3D"external text"=20
  =
title=3Dhttp://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Real_numbe=
rs_3.html=20
  =
href=3D"http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Real_numbe=
rs_3.html"=20
  rel=3Dnofollow>The real numbers: Attempts to understand</A> </LI></UL>
<TABLE class=3Dnavbox cellSpacing=3D0>
  <TBODY>
  <TR>
    <TD=20
    style=3D"PADDING-RIGHT: 2px; PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; =
PADDING-TOP: 2px">
      <TABLE class=3D"nowraplinks collapsible autocollapse"=20
      style=3D"BACKGROUND: none transparent scroll repeat 0% 0%; WIDTH: =
100%"=20
      cellSpacing=3D0>
        <TBODY>
        <TR>
          <TH class=3Dnavbox-title colSpan=3D2>
            <DIV style=3D"FLOAT: left; WIDTH: 6em; TEXT-ALIGN: left">
            <DIV class=3D"noprint plainlinks navbar"=20
            style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 0px; FONT-WEIGHT: =
normal; FONT-SIZE: xx-small; BACKGROUND: none transparent scroll repeat =
0% 0%; PADDING-BOTTOM: 0px; BORDER-TOP-STYLE: none; PADDING-TOP: 0px; =
BORDER-RIGHT-STYLE: none; BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: =
none"><A=20
            title=3D"Template:Number systems"=20
            =
href=3D"http://en.wikipedia.org/wiki/Template:Number_systems"><SPAN=20
            title=3D"View this template"=20
            style=3D"BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; =
BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: =
none">v</SPAN></A>&nbsp;<SPAN=20
            style=3D"FONT-SIZE: 80%">=E2=80=A2</SPAN>&nbsp;<A=20
            title=3D"Template talk:Number systems"=20
            =
href=3D"http://en.wikipedia.org/wiki/Template_talk:Number_systems"><SPAN =

            title=3D"Discuss this template"=20
            style=3D"BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; =
BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: =
none">d</SPAN></A>&nbsp;<SPAN=20
            style=3D"FONT-SIZE: 80%">=E2=80=A2</SPAN>&nbsp;<A =
class=3D"external text"=20
            =
title=3Dhttp://en.wikipedia.org/w/index.php?title=3DTemplate:Number_syste=
ms&amp;action=3Dedit=20
            =
href=3D"http://en.wikipedia.org/w/index.php?title=3DTemplate:Number_syste=
ms&amp;action=3Dedit"=20
            rel=3Dnofollow><SPAN title=3D"Edit this template"=20
            style=3D"BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; =
BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: =
none">e</SPAN></A></DIV></DIV><SPAN=20
            class=3D"" style=3D"FONT-SIZE: 110%"><A title=3D"Number =
system"=20
            href=3D"http://en.wikipedia.org/wiki/Number_system">Number=20
            systems</A></SPAN></TH></TR>
        <TR style=3D"HEIGHT: 2px">
          <TD></TD></TR>
        <TR>
          <TD class=3Dnavbox-group>Basic</TD>
          <TD class=3D"navbox-list navbox-odd"=20
          style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 0px; =
PADDING-BOTTOM: 0px; BORDER-LEFT: 2px solid; WIDTH: 100%; PADDING-TOP: =
0px; TEXT-ALIGN: left">
            <DIV=20
            style=3D"PADDING-RIGHT: 0.25em; PADDING-LEFT: 0.25em; =
PADDING-BOTTOM: 0em; PADDING-TOP: 0em"><A=20
            title=3D"Natural number"=20
            href=3D"http://en.wikipedia.org/wiki/Natural_number">Natural =

            numbers</A>&nbsp;(<IMG class=3Dtex =
alt=3D\scriptstyle\mathbb{N}=20
            =
src=3D"http://upload.wikimedia.org/math/6/f/8/6f8608a3b5fde50a63beda7633a=
8ce73.png">)&nbsp;<B>=C2=B7</B>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3DInteger=20
            href=3D"http://en.wikipedia.org/wiki/Integer">Integers</A> =
(<IMG=20
            class=3Dtex alt=3D\scriptstyle\mathbb{Z}=20
            =
src=3D"http://upload.wikimedia.org/math/5/6/2/562cdc624b2d81af78bfc9e4866=
a44eb.png">)</SPAN>&nbsp;<B>=C2=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3D"Rational number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Rational_number">Rational=20
            numbers</A> (<IMG class=3Dtex alt=3D\scriptstyle\mathbb{Q}=20
            =
src=3D"http://upload.wikimedia.org/math/9/e/3/9e380593b0c0b8c670a83ac53f9=
95138.png">)</SPAN>&nbsp;<B>=C2=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><A title=3D"Irrational =
number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Irrational_number">Irrational=20
            numbers</A>&nbsp;<B>=C2=B7</B></SPAN> <SPAN=20
            style=3D"WHITE-SPACE: nowrap"><SPAN=20
            style=3D"WHITE-SPACE: nowrap"><STRONG class=3Dselflink>Real=20
            numbers</STRONG> (<IMG class=3Dtex =
alt=3D\scriptstyle\mathbb{R}=20
            =
src=3D"http://upload.wikimedia.org/math/8/3/9/8391582a36371405fd2e90d5012=
7651c.png">)</SPAN>&nbsp;<B>=C2=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3D"Imaginary number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Imaginary_number">Imaginary=20
            numbers</A> (<IMG class=3Dtex alt=3D\scriptstyle\mathbb{I}\, =

            =
src=3D"http://upload.wikimedia.org/math/7/e/e/7ee5f6ba4cdc959896df1c44a5a=
dfefd.png">)</SPAN>&nbsp;<B>=C2=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3D"Complex number"=20
            href=3D"http://en.wikipedia.org/wiki/Complex_number">Complex =

            numbers</A> (<IMG class=3Dtex alt=3D\scriptstyle\mathbb{C}=20
            =
src=3D"http://upload.wikimedia.org/math/e/7/8/e7887a11d173ff6b8e91b77275c=
4a62e.png">)</SPAN>&nbsp;<B>=C2=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3D"Algebraic number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Algebraic_number">Algebraic=20
            numbers</A> (<IMG class=3Dtex =
alt=3D\scriptstyle\overline{\mathbb{Q}}=20
            =
src=3D"http://upload.wikimedia.org/math/f/b/a/fba2a69138fd11c79f8d5aab0ef=
16999.png">)</SPAN>&nbsp;<B>=C2=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><A =
title=3D"Transcendental number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Transcendental_number">Transcendenta=
l=20
            numbers</A>&nbsp;<B>=C2=B7</B></SPAN> <SPAN=20
            style=3D"WHITE-SPACE: nowrap"><SPAN style=3D"WHITE-SPACE: =
nowrap"><A=20
            title=3DQuaternion=20
            =
href=3D"http://en.wikipedia.org/wiki/Quaternion">Quaternions</A> (<IMG=20
            class=3Dtex alt=3D\scriptstyle\mathbb{H}=20
            =
src=3D"http://upload.wikimedia.org/math/a/9/4/a94a998049071ef0d7e42a64e96=
768f4.png">)</SPAN>&nbsp;<B>=C2=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3DOctonion=20
            href=3D"http://en.wikipedia.org/wiki/Octonion">Octonions</A> =
(<IMG=20
            class=3Dtex alt=3D\scriptstyle\mathbb{O}=20
            =
src=3D"http://upload.wikimedia.org/math/9/4/d/94d78ea63383ccea41b99b4e93b=
53ec3.png">)</SPAN>&nbsp;<B>=C2=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3DSedenion=20
            href=3D"http://en.wikipedia.org/wiki/Sedenion">Sedenions</A> =
(<IMG=20
            class=3Dtex alt=3D\scriptstyle\mathbb{S}=20
            =
src=3D"http://upload.wikimedia.org/math/f/4/4/f44bcdf3323c687ab2c36b5a729=
26f5e.png">)</SPAN>&nbsp;<B>=C2=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><A=20
            title=3D"Cayley=E2=80=93Dickson construction"=20
            =
href=3D"http://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction"=
>Cayley=E2=80=93Dickson=20
            construction</A>&nbsp;<B>=C2=B7</B></SPAN> <SPAN=20
            style=3D"WHITE-SPACE: nowrap"><SPAN style=3D"WHITE-SPACE: =
nowrap"><A=20
            title=3D"Split-complex number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Split-complex_number">Split-complex =

            numbers</A></SPAN></SPAN></DIV></TD></TR>
        <TR style=3D"HEIGHT: 2px">
          <TD></TD></TR>
        <TR>
          <TD class=3Dnavbox-group>Complex<BR>extensions</TD>
          <TD class=3D"navbox-list navbox-even"=20
          style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 0px; =
PADDING-BOTTOM: 0px; BORDER-LEFT: 2px solid; WIDTH: 100%; PADDING-TOP: =
0px; TEXT-ALIGN: left">
            <DIV=20
            style=3D"PADDING-RIGHT: 0.25em; PADDING-LEFT: 0.25em; =
PADDING-BOTTOM: 0em; PADDING-TOP: 0em"><A=20
            title=3D"Bicomplex number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Bicomplex_number">Bicomplex=20
            numbers</A>&nbsp;<B>=C2=B7</B> <SPAN style=3D"WHITE-SPACE: =
nowrap"><A=20
            title=3DBiquaternion=20
            =
href=3D"http://en.wikipedia.org/wiki/Biquaternion">Biquaternions</A>&nbsp=
;<B>=C2=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><A =
title=3DSplit-quaternion=20
            =
href=3D"http://en.wikipedia.org/wiki/Split-quaternion">Split-quaternions<=
/A>&nbsp;<B>=C2=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><A title=3DTessarine=20
            =
href=3D"http://en.wikipedia.org/wiki/Tessarine">Tessarines</A>&nbsp;<B>=C2=
=B7</B></SPAN>=20
            <SPAN style=3D"WHITE-SPACE: nowrap"><A title=3D"Hypercomplex =
number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Hypercomplex_number">Hypercomplex=20
            numbers</A>&nbsp;<B>=C2=B7</B></SPAN> <SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3D"Musean =
hypernumber"=20
            =
href=3D"http://en.wikipedia.org/wiki/Musean_hypernumber">Musean=20
            hypernumbers</A>&nbsp;<B>=C2=B7</B></SPAN> <SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3D"Superreal number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Superreal_number">Superreal=20
            numbers</A>&nbsp;<B>=C2=B7</B></SPAN> <SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3D"Hyperreal number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Hyperreal_number">Hyperreal=20
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            style=3D"WHITE-SPACE: nowrap"><A title=3D"Supernatural =
numbers"=20
            =
href=3D"http://en.wikipedia.org/wiki/Supernatural_numbers">Supernatural=20
            numbers</A>&nbsp;<B>=C2=B7</B></SPAN> <SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3D"Surreal number"=20
            href=3D"http://en.wikipedia.org/wiki/Surreal_number">Surreal =

            numbers</A></SPAN></DIV></TD></TR>
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          <TD></TD></TR>
        <TR>
          <TD class=3Dnavbox-group>Other extensions</TD>
          <TD class=3D"navbox-list navbox-odd"=20
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PADDING-BOTTOM: 0px; BORDER-LEFT: 2px solid; WIDTH: 100%; PADDING-TOP: =
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            <DIV=20
            style=3D"PADDING-RIGHT: 0.25em; PADDING-LEFT: 0.25em; =
PADDING-BOTTOM: 0em; PADDING-TOP: 0em"><A=20
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            href=3D"http://en.wikipedia.org/wiki/Dual_number">Dual=20
            numbers</A>&nbsp;<B>=C2=B7</B> <SPAN style=3D"WHITE-SPACE: =
nowrap"><A=20
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            =
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            numbers</A>&nbsp;<B>=C2=B7</B></SPAN> <SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A class=3Dmw-redirect=20
            title=3D"Extended real number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Extended_real_number">Extended=20
            real numbers</A>&nbsp;<B>=C2=B7</B></SPAN> <SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3D"Cardinal number"=20
            =
href=3D"http://en.wikipedia.org/wiki/Cardinal_number">Cardinal=20
            numbers</A>&nbsp;<B>=C2=B7</B></SPAN> <SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3D"Ordinal number"=20
            href=3D"http://en.wikipedia.org/wiki/Ordinal_number">Ordinal =

            numbers</A>&nbsp;<B>=C2=B7</B></SPAN> <SPAN=20
            style=3D"WHITE-SPACE: nowrap"><A title=3D"P-adic number"=20
            =
href=3D"http://en.wikipedia.org/wiki/P-adic_number"><I>p</I>-adic=20
            =
numbers</A></SPAN></DIV></TD></TR></TBODY></TABLE></TD></TR></TBODY></TAB=
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=D0=BA=D0=B0=D1=8F</A>=20

  <LI class=3Dinterwiki-bs><A=20
  href=3D"http://bs.wikipedia.org/wiki/Realan_broj">Bosanski</A>=20
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  =
href=3D"http://bg.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B0%D0%BB%D0%BD%D0%BE=
_%D1%87%D0%B8%D1%81%D0%BB%D0%BE">=D0=91=D1=8A=D0=BB=D0=B3=D0=B0=D1=80=D1=81=
=D0=BA=D0=B8</A>=20

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5%D0%B8%D1%81%D0%B5%D0%BF%C4%95">=D0=A7=D3=91=D0=B2=D0=B0=D1=88=D0=BB=D0=B0=
</A>=20

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1%D7%A4%D7%A8%D7%99%D7%9D_%D7%94%D7%9E%D7%9E%D7%A9%D7%99%D7%99%D7%9D">=D7=
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%E1%83%95%E1%83%98">=E1=83=A5=E1=83=90=E1=83=A0=E1=83=97=E1=83=A3=E1=83=9A=
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	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(audio.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.wma'].external {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(audio.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.WMA'].external {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(audio.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
.link-audio {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(audio.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.ogm'].external {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(video.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.OGM'].external {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(video.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.avi'].external {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(video.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.AVI'].external {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(video.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.mpeg'].external {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(video.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.MPEG'].external {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(video.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.mpg'].external {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(video.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.MPG'].external {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(video.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
.link-video {
	PADDING-RIGHT: 13px; PADDING-LEFT: 13px; BACKGROUND: url(video.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.pdf'].external {
	PADDING-RIGHT: 12px; PADDING-LEFT: 12px; BACKGROUND: url(document.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href$=3D'.PDF'].external {
	PADDING-RIGHT: 12px; PADDING-LEFT: 12px; BACKGROUND: url(document.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href*=3D'.pdf#'].external {
	PADDING-RIGHT: 12px; PADDING-LEFT: 12px; BACKGROUND: url(document.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href*=3D'.PDF#'].external {
	PADDING-RIGHT: 12px; PADDING-LEFT: 12px; BACKGROUND: url(document.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href*=3D'.pdf?'].external {
	PADDING-RIGHT: 12px; PADDING-LEFT: 12px; BACKGROUND: url(document.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
#bodyContent A[href*=3D'.PDF?'].external {
	PADDING-RIGHT: 12px; PADDING-LEFT: 12px; BACKGROUND: url(document.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
.link-document {
	PADDING-RIGHT: 12px; PADDING-LEFT: 12px; BACKGROUND: url(document.png) =
no-repeat right center; PADDING-BOTTOM: 0px; PADDING-TOP: 0px
}
.rtl #bodyContent A.external {
	PADDING-RIGHT: 0px; BACKGROUND-POSITION: left 50%
}
.rtl A.feedlink {
	PADDING-RIGHT: 16px; BACKGROUND-POSITION: right 50%; PADDING-LEFT: 0px
}
.ltr #bodyContent A.external {
	PADDING-LEFT: 0px
}
#bodyContent A.extiw {
	COLOR: #36b
}
#bodyContent A.extiw:active {
	COLOR: #36b
}
#bodyContent A.external {
	COLOR: #36b
}
.portlet {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; FLOAT: none; PADDING-BOTTOM: =
0px; MARGIN: 0px 0px 0.5em; OVERFLOW: hidden; WIDTH: 11.6em; =
BORDER-TOP-STYLE: none; PADDING-TOP: 0px; BORDER-RIGHT-STYLE: none; =
BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: none
}
.portlet H4 {
	FONT-WEIGHT: normal; FONT-SIZE: 95%; WHITE-SPACE: nowrap
}
.portlet H5 {
	PADDING-RIGHT: 1em; DISPLAY: inline; PADDING-LEFT: 0.5em; FONT-WEIGHT: =
normal; FONT-SIZE: 91%; BACKGROUND: none transparent scroll repeat 0% =
0%; PADDING-BOTTOM: 0px; TEXT-TRANSFORM: lowercase; PADDING-TOP: 0px; =
WHITE-SPACE: nowrap; HEIGHT: 1em
}
.portlet H6 {
	BORDER-RIGHT: #2f6fab 1px solid; PADDING-RIGHT: 1em; BORDER-TOP: =
#2f6fab 1px solid; DISPLAY: block; PADDING-LEFT: 1em; FONT-WEIGHT: =
normal; FONT-SIZE: 1em; BACKGROUND: #ffae2e; PADDING-BOTTOM: 0px; =
TEXT-TRANSFORM: lowercase; BORDER-LEFT: #2f6fab 1px solid; PADDING-TOP: =
0px; BORDER-BOTTOM: #2f6fab 1px; WHITE-SPACE: nowrap; HEIGHT: 1.2em
}
.pBody {
	BORDER-RIGHT: #aaa 1px solid; PADDING-RIGHT: 0.8em; BORDER-TOP: #aaa =
1px solid; PADDING-LEFT: 0.5em; FONT-SIZE: 95%; PADDING-BOTTOM: 0.3em; =
BORDER-LEFT: #aaa 1px solid; COLOR: black; PADDING-TOP: 0px; =
BORDER-BOTTOM: #aaa 1px solid; BORDER-COLLAPSE: collapse; =
BACKGROUND-COLOR: white
}
.portlet H1 {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; PADDING-BOTTOM: 0px; MARGIN: =
0px; PADDING-TOP: 0px
}
.portlet H2 {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; PADDING-BOTTOM: 0px; MARGIN: =
0px; PADDING-TOP: 0px
}
.portlet H3 {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; PADDING-BOTTOM: 0px; MARGIN: =
0px; PADDING-TOP: 0px
}
.portlet H4 {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; PADDING-BOTTOM: 0px; MARGIN: =
0px; PADDING-TOP: 0px
}
.portlet UL {
	FONT-SIZE: 95%; LIST-STYLE-IMAGE: url(bullet.gif); LINE-HEIGHT: 1.5em; =
LIST-STYLE-TYPE: square
}
.portlet LI {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; PADDING-BOTTOM: 0px; MARGIN: =
0px; PADDING-TOP: 0px
}
#p-logo {
	Z-INDEX: 3; LEFT: 0px; OVERFLOW: visible; WIDTH: 12em; POSITION: =
absolute; TOP: 0px; HEIGHT: 155px
}
#p-logo H5 {
	DISPLAY: none
}
#p-logo A {
	BACKGROUND-POSITION: 35% 50%; DISPLAY: block; WIDTH: 12.2em; =
BACKGROUND-REPEAT: no-repeat; HEIGHT: 155px; TEXT-DECORATION: none
}
#p-logo A:hover {
	BACKGROUND-POSITION: 35% 50%; DISPLAY: block; WIDTH: 12.2em; =
BACKGROUND-REPEAT: no-repeat; HEIGHT: 155px; TEXT-DECORATION: none
}
#p-search {
	Z-INDEX: 3; POSITION: relative
}
INPUT.searchButton {
	MARGIN-TOP: 1px; FONT-SIZE: 95%
}
#searchGoButton {
	PADDING-RIGHT: 0.5em; PADDING-LEFT: 0.5em; FONT-WEIGHT: bold
}
#searchInput {
	FONT-SIZE: 95%; MARGIN: 0px; WIDTH: 10.9em
}
#p-search .pBody {
	PADDING-RIGHT: 0.4em; PADDING-LEFT: 0.4em; PADDING-BOTTOM: 0.4em; =
PADDING-TOP: 0.5em; TEXT-ALIGN: center
}
#p-search #searchform DIV DIV {
	MARGIN-TOP: 0.4em; FONT-SIZE: 95%
}
#p-personal {
	LEFT: 0px; POSITION: absolute; TOP: 0px
}
#p-personal {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; BACKGROUND: none transparent =
scroll repeat 0% 0%; PADDING-BOTTOM: 0px; MARGIN: 0px; OVERFLOW: =
visible; WIDTH: 100%; BORDER-TOP-STYLE: none; LINE-HEIGHT: 1.2em; =
PADDING-TOP: 0px; BORDER-RIGHT-STYLE: none; WHITE-SPACE: nowrap; =
BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: none
}
#p-personal H5 {
	DISPLAY: none
}
#p-personal .portlet {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; BACKGROUND: none transparent =
scroll repeat 0% 0%; PADDING-BOTTOM: 0px; MARGIN: 0px; OVERFLOW: =
visible; BORDER-TOP-STYLE: none; PADDING-TOP: 0px; BORDER-RIGHT-STYLE: =
none; BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: none
}
#p-personal .pBody {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; BACKGROUND: none transparent =
scroll repeat 0% 0%; PADDING-BOTTOM: 0px; MARGIN: 0px; OVERFLOW: =
visible; BORDER-TOP-STYLE: none; PADDING-TOP: 0px; BORDER-RIGHT-STYLE: =
none; BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: none
}
#p-personal UL {
	PADDING-RIGHT: 2em; PADDING-LEFT: 3em; BACKGROUND: none transparent =
scroll repeat 0% 0%; PADDING-BOTTOM: 0px; MARGIN: 0px; CURSOR: default; =
COLOR: #2f6fab; BORDER-TOP-STYLE: none; LINE-HEIGHT: 1.4em; PADDING-TOP: =
0px; BORDER-RIGHT-STYLE: none; BORDER-LEFT-STYLE: none; LIST-STYLE-TYPE: =
none; TEXT-ALIGN: right; BORDER-BOTTOM-STYLE: none
}
#p-personal LI {
	PADDING-RIGHT: 0px; DISPLAY: inline; PADDING-LEFT: 0px; BACKGROUND: =
none transparent scroll repeat 0% 0%; PADDING-BOTTOM: 0px; MARGIN-LEFT: =
1em; COLOR: #2f6fab; BORDER-TOP-STYLE: none; LINE-HEIGHT: 1.2em; =
PADDING-TOP: 0px; BORDER-RIGHT-STYLE: none; BORDER-LEFT-STYLE: none; =
BORDER-BOTTOM-STYLE: none
}
#p-personal LI A {
	BACKGROUND: none transparent scroll repeat 0% 0%; PADDING-BOTTOM: =
0.2em; COLOR: #005896; TEXT-DECORATION: none
}
#p-personal LI A:hover {
	PADDING-BOTTOM: 0.2em; BACKGROUND-COLOR: white; TEXT-DECORATION: none
}
#p-personal LI.active A:hover {
	BACKGROUND-COLOR: transparent
}
LI#pt-userpage {
	PADDING-LEFT: 20px; BACKGROUND: url(user.gif) no-repeat left top; =
TEXT-TRANSFORM: none
}
LI#pt-anonuserpage {
	PADDING-LEFT: 20px; BACKGROUND: url(user.gif) no-repeat left top; =
TEXT-TRANSFORM: none
}
LI#pt-login {
	PADDING-LEFT: 20px; BACKGROUND: url(user.gif) no-repeat left top; =
TEXT-TRANSFORM: none
}
#p-personal UL {
	TEXT-TRANSFORM: lowercase
}
#p-personal LI.active {
	FONT-WEIGHT: bold
}
#p-cactions {
	PADDING-LEFT: 1em; FONT-SIZE: 95%; BACKGROUND: none transparent scroll =
repeat 0% 0%; LEFT: 11.5em; MARGIN: 0px; OVERFLOW: visible; WIDTH: 76%; =
LINE-HEIGHT: 1.1em; WHITE-SPACE: nowrap; LIST-STYLE-TYPE: none; =
POSITION: absolute; TOP: 1.3em; BORDER-COLLAPSE: collapse
}
#p-cactions UL {
	LIST-STYLE-TYPE: none
}
#p-cactions LI {
	BORDER-RIGHT: #aaa 1px solid; PADDING-RIGHT: 0px; BORDER-TOP: #aaa 1px =
solid; DISPLAY: inline; PADDING-LEFT: 0px; BACKGROUND: white; =
PADDING-BOTTOM: 0.1em; MARGIN: 0px 0.3em 0px 0px; OVERFLOW: visible; =
BORDER-LEFT: #aaa 1px solid; PADDING-TOP: 0px; BORDER-BOTTOM: #aaa 1px
}
#p-cactions LI.selected {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; FONT-WEIGHT: bold; =
BORDER-LEFT-COLOR: #fabd23; BORDER-BOTTOM-COLOR: #fabd23; =
PADDING-BOTTOM: 0.2em; BORDER-TOP-COLOR: #fabd23; PADDING-TOP: 0px; =
BORDER-RIGHT-COLOR: #fabd23
}
#p-cactions LI A {
	PADDING-RIGHT: 0.8em; PADDING-LEFT: 0.8em; PADDING-BOTTOM: 0.3em; =
MARGIN: 0px; COLOR: #002bb8; BORDER-TOP-STYLE: none; PADDING-TOP: 0px; =
BORDER-RIGHT-STYLE: none; BORDER-LEFT-STYLE: none; POSITION: relative; =
BACKGROUND-COLOR: #fbfbfb; TEXT-DECORATION: none; BORDER-BOTTOM-STYLE: =
none
}
#p-cactions LI.selected A {
	PADDING-RIGHT: 1em! important; PADDING-LEFT: 1em! important; Z-INDEX: =
3; PADDING-BOTTOM: 0.2em! important; PADDING-TOP: 0px! important; =
BACKGROUND-COLOR: white
}
#p-cactions .new A {
	COLOR: #ba0000
}
#p-cactions LI A:hover {
	Z-INDEX: 3; BACKGROUND-COLOR: white; TEXT-DECORATION: none
}
#p-cactions H5 {
	DISPLAY: none
}
#p-cactions LI.istalk {
	MARGIN-RIGHT: 0px
}
#p-cactions LI.istalk A {
	PADDING-RIGHT: 0.5em
}
#p-cactions #ca-addsection A {
	PADDING-RIGHT: 0.4em; PADDING-LEFT: 0.4em
}
LI#ca-talk {
	MARGIN-RIGHT: 1.6em
}
LI#ca-watch {
	MARGIN-LEFT: 1.6em
}
LI#ca-unwatch {
	MARGIN-LEFT: 1.6em
}
LI#ca-varlang-0 {
	MARGIN-LEFT: 1.6em
}
LI#ca-print {
	MARGIN-LEFT: 1.6em
}
#p-cactions .pBody {
	BORDER-TOP-WIDTH: 0px; PADDING-RIGHT: 0px; PADDING-LEFT: 0px; =
BORDER-LEFT-WIDTH: 0px; FONT-SIZE: 1em; BORDER-BOTTOM-WIDTH: 0px; =
PADDING-BOTTOM: 0px; PADDING-TOP: 0px; BACKGROUND-COLOR: transparent; =
BORDER-RIGHT-WIDTH: 0px
}
#p-cactions .hiddenStructure {
	DISPLAY: none
}
#p-cactions LI A {
	TEXT-TRANSFORM: lowercase
}
#p-lang {
	Z-INDEX: 3; POSITION: relative
}
.capitalize-all-nouns .portlet H5 {
	TEXT-TRANSFORM: none
}
.capitalize-all-nouns .portlet H6 {
	TEXT-TRANSFORM: none
}
.capitalize-all-nouns #p-personal UL {
	TEXT-TRANSFORM: none
}
.capitalize-all-nouns #p-cactions UL LI A {
	TEXT-TRANSFORM: none
}
#t-ispermalink {
	COLOR: #999
}
#t-iscite {
	COLOR: #999
}
#footer {
	PADDING-RIGHT: 0px; BORDER-TOP: #fabd23 1px solid; PADDING-LEFT: 0px; =
FONT-SIZE: 90%; PADDING-BOTTOM: 1.2em; MARGIN: 0.6em 0px 1em; =
PADDING-TOP: 0.4em; BORDER-BOTTOM: #fabd23 1px solid; BACKGROUND-COLOR: =
white; TEXT-ALIGN: center
}
#footer LI {
	DISPLAY: inline; MARGIN: 0px 1.3em
}
#f-poweredbyico {
	MARGIN: 0px 8px; POSITION: relative; TOP: -2px
}
#f-copyrightico {
	MARGIN: 0px 8px; POSITION: relative; TOP: -2px
}
#f-poweredbyico {
	FLOAT: right; HEIGHT: 1%
}
#f-copyrightico {
	FLOAT: left; HEIGHT: 1%
}
.mw-htmlform-submit {
	PADDING-RIGHT: 0.3em; PADDING-LEFT: 0.3em; FONT-WEIGHT: bold; =
MARGIN-RIGHT: 2em
}
#preftoc {
	CLEAR: both; PADDING-RIGHT: 0px; PADDING-LEFT: 0px; PADDING-BOTTOM: =
0px; MARGIN: 0px; WIDTH: 100%; PADDING-TOP: 0px
}
#preftoc LI {
	COLOR: #000; BACKGROUND-COLOR: #f0f0f0
}
#preftoc LI {
	BORDER-RIGHT: #716f64 1px solid; PADDING-RIGHT: 0px; BORDER-TOP: #fff =
1px solid; PADDING-LEFT: 0px; Z-INDEX: 3; FLOAT: left; LIST-STYLE-IMAGE: =
none; PADDING-BOTTOM: 3px; MARGIN: 1px -2px 1px 2px; BORDER-LEFT: #fff =
1px solid; PADDING-TOP: 2px; BORDER-BOTTOM: #fff 0px solid; WHITE-SPACE: =
nowrap; LIST-STYLE-TYPE: none; POSITION: relative
}
#preftoc LI.selected {
	BORDER-RIGHT: #aaa 1px solid; BORDER-TOP: #aaa 1px solid; FONT-WEIGHT: =
bold; BORDER-LEFT: #aaa 1px solid; CURSOR: default; MARGIN-RIGHT: -3px; =
PADDING-TOP: 2px; BORDER-BOTTOM: #aaa 1px; TOP: 1px; BACKGROUND-COLOR: =
#f9f9f9
}
#preftoc > LI.selected {
	TOP: 2px
}
#preftoc A {
	PADDING-RIGHT: 0.7em; DISPLAY: block; PADDING-LEFT: 0.7em; =
PADDING-BOTTOM: 0px; COLOR: #000; PADDING-TOP: 0px; POSITION: relative; =
TEXT-DECORATION: none
}
#preftoc A:active {
	PADDING-RIGHT: 0.7em; DISPLAY: block; PADDING-LEFT: 0.7em; =
PADDING-BOTTOM: 0px; COLOR: #000; PADDING-TOP: 0px; POSITION: relative; =
TEXT-DECORATION: none
}
#preftoc LI.selected A {
	CURSOR: default; TEXT-DECORATION: none
}
#preferences {
	CLEAR: both; BORDER-RIGHT: #aaa 1px solid; PADDING-RIGHT: 1.5em; =
BORDER-TOP: #aaa 1px solid; PADDING-LEFT: 1.5em; PADDING-BOTTOM: 1.5em; =
MARGIN: 0px; BORDER-LEFT: #aaa 1px solid; PADDING-TOP: 1.5em; =
BORDER-BOTTOM: #aaa 1px solid; BACKGROUND-COLOR: #f9f9f9
}
.prefsection {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; PADDING-BOTTOM: 0px; MARGIN: =
0px; BORDER-TOP-STYLE: none; PADDING-TOP: 0px; BORDER-RIGHT-STYLE: none; =
BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: none
}
.prefsection LEGEND {
	FONT-WEIGHT: bold
}
.prefsection TABLE {
	BACKGROUND-COLOR: #f9f9f9
}
.prefsection LEGEND {
	BACKGROUND-COLOR: #f9f9f9
}
.mainLegend {
	DISPLAY: none
}
TD.htmlform-tip {
	PADDING-RIGHT: 2em; PADDING-LEFT: 2em; FONT-SIZE: x-small; =
PADDING-BOTTOM: 0.2em; COLOR: #666; PADDING-TOP: 0.2em
}
.preferences-login {
	CLEAR: both; MARGIN-BOTTOM: 1.5em
}
.prefcache {
	MARGIN-TOP: 2em; FONT-SIZE: 90%
}
DIV#userloginForm FORM {
	CLEAR: both; BORDER-RIGHT: #aaa 1px solid; PADDING-RIGHT: 2em; =
BORDER-TOP: #aaa 1px solid; PADDING-LEFT: 2em; FLOAT: left; =
PADDING-BOTTOM: 1.5em; MARGIN: 0px 3em 1em 0px; BORDER-LEFT: #aaa 1px =
solid; PADDING-TOP: 1.5em; BORDER-BOTTOM: #aaa 1px solid; =
BACKGROUND-COLOR: #f9f9f9
}
DIV#userlogin FORM#userlogin2 {
	CLEAR: both; BORDER-RIGHT: #aaa 1px solid; PADDING-RIGHT: 2em; =
BORDER-TOP: #aaa 1px solid; PADDING-LEFT: 2em; FLOAT: left; =
PADDING-BOTTOM: 1.5em; MARGIN: 0px 3em 1em 0px; BORDER-LEFT: #aaa 1px =
solid; PADDING-TOP: 1.5em; BORDER-BOTTOM: #aaa 1px solid; =
BACKGROUND-COLOR: #f9f9f9
}
.rtl DIV#userloginForm FORM {
	FLOAT: right
}
.rtl DIV#userlogin FORM#userlogin2 {
	FLOAT: right
}
DIV#userloginForm TABLE {
	BACKGROUND-COLOR: #f9f9f9
}
DIV#userlogin FORM#userlogin2 TABLE {
	BACKGROUND-COLOR: #f9f9f9
}
DIV#userloginForm H2 {
	PADDING-TOP: 0px
}
DIV#userlogin FORM#userlogin2 H2 {
	PADDING-TOP: 0px
}
DIV#userlogin .captcha {
	BORDER-RIGHT: #bbb 1px solid; PADDING-RIGHT: 2em; BORDER-TOP: #bbb 1px =
solid; PADDING-LEFT: 2em; PADDING-BOTTOM: 1.5em; BORDER-LEFT: #bbb 1px =
solid; PADDING-TOP: 1.5em; BORDER-BOTTOM: #bbb 1px solid; =
BACKGROUND-COLOR: white
}
DIV#userloginForm .captcha {
	BORDER-RIGHT: #bbb 1px solid; PADDING-RIGHT: 2em; BORDER-TOP: #bbb 1px =
solid; PADDING-LEFT: 2em; PADDING-BOTTOM: 1.5em; BORDER-LEFT: #bbb 1px =
solid; PADDING-TOP: 1.5em; BORDER-BOTTOM: #bbb 1px solid; =
BACKGROUND-COLOR: white
}
#loginend {
	CLEAR: both
}
#signupend {
	CLEAR: both
}
#userloginprompt {
	FONT-SIZE: 85%
}
#languagelinks {
	FONT-SIZE: 85%
}
#login-sectiontip {
	FONT-SIZE: 85%; LINE-HEIGHT: 1.2; PADDING-TOP: 2em
}
#userlogin .loginText {
	WIDTH: 12em
}
#userlogin .loginPassword {
	WIDTH: 12em
}
#userloginlink A {
	FONT-WEIGHT: bold
}
#wpLoginattempt {
	FONT-WEIGHT: bold
}
#wpCreateaccount {
	FONT-WEIGHT: bold
}
* > HTML #p-cactions LI {
	BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; BORDER-LEFT-STYLE: =
none; BORDER-BOTTOM-STYLE: none
}
* > HTML #p-cactions LI A {
	BORDER-RIGHT: #aaa 1px solid; BORDER-TOP: #aaa 1px solid; BORDER-LEFT: =
#aaa 1px solid; BORDER-BOTTOM: #aaa 1px
}
* > HTML #p-cactions LI.selected A {
	BORDER-LEFT-COLOR: #fabd23; BORDER-BOTTOM-COLOR: #fabd23; =
BORDER-TOP-COLOR: #fabd23; BORDER-RIGHT-COLOR: #fabd23
}
* > HTML #f-poweredbyico {
	WIDTH: 88px
}
* > HTML #f-copyrightico {
	WIDTH: 88px
}
* > HTML #bodyContent {
	OVERFLOW-X: auto; PADDING-BOTTOM: 25px; WIDTH: 100%
}
* > HTML #bodyContent PRE {
	OVERFLOW-X: auto; PADDING-BOTTOM: 25px; WIDTH: 100%
}
* HTML #footer {
	MARGIN-TOP: 0px
}
* HTML #column-content {
	DISPLAY: inline; MARGIN-BOTTOM: 0px
}
* HTML DIV.editsection {
	FONT-SIZE: smaller
}
#pagehistory LI.selected {
	POSITION: relative
}
* > HTML #column-content {
	FLOAT: none
}
* > HTML #column-one {
	LEFT: 0px; POSITION: absolute; TOP: 0px
}
* > HTML #footer {
	MARGIN-LEFT: 13.2em
}
.redirectText {
	FONT-SIZE: 150%; MARGIN: 5px
}
.printfooter {
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}
DIV.patrollink {
	CLEAR: both
}
SPAN.newpage {
	FONT-WEIGHT: bold
}
SPAN.minor {
	FONT-WEIGHT: bold
}
SPAN.bot {
	FONT-WEIGHT: bold
}
.sharedUploadNotice {
	FONT-STYLE: italic
}
SPAN.updatedmarker {
	COLOR: black; BACKGROUND-COLOR: #0f0
}
TABLE.gallery {
	BORDER-RIGHT: #ccc 1px solid; PADDING-RIGHT: 2px; BORDER-TOP: #ccc 1px =
solid; PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; MARGIN: 2px; BORDER-LEFT: =
#ccc 1px solid; PADDING-TOP: 2px; BORDER-BOTTOM: #ccc 1px solid; =
BACKGROUND-COLOR: white
}
TABLE.gallery TR {
	VERTICAL-ALIGN: top
}
TABLE.gallery TD {
	BORDER-RIGHT: white 2px solid; BORDER-TOP: white 2px solid; =
VERTICAL-ALIGN: top; BORDER-LEFT: white 2px solid; BORDER-BOTTOM: white =
2px solid; BACKGROUND-COLOR: #f9f9f9
}
TABLE.gallery TD.galleryheader {
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}
TABLE.gallery CAPTION {
	FONT-WEIGHT: bold
}
DIV.gallerybox {
	MARGIN: 2px
}
DIV.gallerybox DIV.thumb {
	BORDER-RIGHT: #ccc 1px solid; BORDER-TOP: #ccc 1px solid; MARGIN: 2px; =
BORDER-LEFT: #ccc 1px solid; BORDER-BOTTOM: #ccc 1px solid; TEXT-ALIGN: =
center
}
DIV.gallerytext {
	PADDING-RIGHT: 4px; PADDING-LEFT: 4px; FONT-SIZE: 94%; PADDING-BOTTOM: =
2px; OVERFLOW: hidden; PADDING-TOP: 2px
}
SPAN.comment {
	FONT-STYLE: italic
}
SPAN.changedby {
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}
.previewnote {
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}
.previewnote P {
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}
.editExternally {
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solid; MARGIN-TOP: 0.5em; PADDING-LEFT: 3px; FONT-SIZE: small; FLOAT: =
left; PADDING-BOTTOM: 3px; BORDER-LEFT: gray 1px solid; PADDING-TOP: =
3px; BORDER-BOTTOM: gray 1px solid; BACKGROUND-COLOR: #ffffff; =
TEXT-ALIGN: center
}
.editExternallyHelp {
	COLOR: gray; FONT-STYLE: italic
}
.toggle {
	MARGIN-LEFT: 2em; TEXT-INDENT: -2em
}
INPUT#wpSummary {
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}
INPUT#wpSave {
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}
INPUT#wpDiff {
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}
#wpSave {
	FONT-WEIGHT: bold
}
TABLE.revisionform_default {
	BORDER-RIGHT: #000000 1px solid; BORDER-TOP: #000000 1px solid; =
BORDER-LEFT: #000000 1px solid; BORDER-BOTTOM: #000000 1px solid
}
TABLE.revisionform_focus {
	BORDER-RIGHT: #000000 1px solid; BORDER-TOP: #000000 1px solid; =
BORDER-LEFT: #000000 1px solid; BORDER-BOTTOM: #000000 1px solid; =
BACKGROUND-COLOR: #00bbff
}
TR.revision_tr_default {
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}
TR.revision_tr_first {
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}
P.revision_saved {
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}
#allmessagestable TH {
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}
#allmessagestable TR.orig {
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}
#allmessagestable TR.new {
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}
#allmessagestable TR.def {
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}
DIV.noarticletext {
	BORDER-RIGHT: #ccc 1px solid; PADDING-RIGHT: 1em; BORDER-TOP: #ccc 1px =
solid; PADDING-LEFT: 1em; BACKGROUND: #fff; PADDING-BOTTOM: 0.2em; =
BORDER-LEFT: #ccc 1px solid; COLOR: #000; PADDING-TOP: 0.2em; =
BORDER-BOTTOM: #ccc 1px solid
}
DIV#searchTargetContainer {
	BACKGROUND: white; LEFT: 10px; WIDTH: 90%; TOP: 10px
}
DIV#searchTarget {
	BORDER-RIGHT: blue 1px solid; PADDING-RIGHT: 3px; BORDER-TOP: blue 1px =
solid; PADDING-LEFT: 3px; BACKGROUND: #f0f0f0; PADDING-BOTTOM: 3px; =
MARGIN: 5px; BORDER-LEFT: blue 1px solid; PADDING-TOP: 3px; =
BORDER-BOTTOM: blue 1px solid
}
DIV#searchTarget UL LI {
	LIST-STYLE-TYPE: none
}
DIV#searchTarget UL LI:unknown {
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}
DIV#searchTargetHide {
	BORDER-RIGHT: black 1px solid; PADDING-RIGHT: 2px; BORDER-TOP: black =
1px solid; PADDING-LEFT: 2px; BACKGROUND: #dcdcdc; FLOAT: right; =
PADDING-BOTTOM: 2px; BORDER-LEFT: black 1px solid; PADDING-TOP: 2px; =
BORDER-BOTTOM: black 1px solid
}
#powersearch P {
	MARGIN-TOP: 0px
}
DIV.multipageimagenavbox {
	BORDER-RIGHT: silver 1px solid; PADDING-RIGHT: 4px; BORDER-TOP: silver =
1px solid; PADDING-LEFT: 4px; BACKGROUND: #f0f0f0; PADDING-BOTTOM: 4px; =
MARGIN: 1em; BORDER-LEFT: silver 1px solid; PADDING-TOP: 4px; =
BORDER-BOTTOM: silver 1px solid
}
DIV.multipageimagenavbox DIV.thumb {
	MARGIN-LEFT: 2em; BORDER-TOP-STYLE: none; MARGIN-RIGHT: 2em; =
BORDER-RIGHT-STYLE: none; BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: =
none
}
DIV.multipageimagenavbox HR {
	MARGIN: 6px
}
TABLE.multipageimage TD {
	TEXT-ALIGN: center
}
.templatesUsed {
	MARGIN-TOP: 1.5em
}
.mw-summary-preview {
	MARGIN: 0.1em 0px
}
DIV.mw-lag-warn-normal {
	PADDING-RIGHT: 3px; PADDING-LEFT: 3px; PADDING-BOTTOM: 3px; MARGIN: 3px =
auto; PADDING-TOP: 3px; TEXT-ALIGN: center
}
DIV.mw-lag-warn-high {
	PADDING-RIGHT: 3px; PADDING-LEFT: 3px; PADDING-BOTTOM: 3px; MARGIN: 3px =
auto; PADDING-TOP: 3px; TEXT-ALIGN: center
}
DIV.mw-lag-warn-normal {
	BORDER-RIGHT: #ffcc66 1px solid; BORDER-TOP: #ffcc66 1px solid; =
BORDER-LEFT: #ffcc66 1px solid; BORDER-BOTTOM: #ffcc66 1px solid; =
BACKGROUND-COLOR: #ffffcc
}
DIV.mw-lag-warn-high {
	BORDER-RIGHT: #ff0033 2px solid; BORDER-TOP: #ff0033 2px solid; =
FONT-WEIGHT: bold; BORDER-LEFT: #ff0033 2px solid; BORDER-BOTTOM: =
#ff0033 2px solid; BACKGROUND-COLOR: #ffcccc
}
.MediaTransformError {
	PADDING-RIGHT: 0.1em; PADDING-LEFT: 0.1em; PADDING-BOTTOM: 0.1em; =
PADDING-TOP: 0.1em; BACKGROUND-COLOR: #ccc
}
.MediaTransformError TD {
	FONT-SIZE: 90%; VERTICAL-ALIGN: middle; TEXT-ALIGN: center
}
.os-suggest {
	FONT-SIZE: 127%
}
.no-text-transform {
	TEXT-TRANSFORM: none
}

------=_NextPart_000_0049_01CA353D.AD380F90
Content-Type: application/octet-stream
Content-Transfer-Encoding: quoted-printable
Content-Location: http://en.wikipedia.org/skins-1.5/chick/main.css?233zz2

BODY {
	PADDING-RIGHT: 0.3em; PADDING-LEFT: 0.3em; PADDING-BOTTOM: 0.3em; =
MARGIN: 0px; COLOR: black; PADDING-TOP: 0.3em; FONT-FAMILY: sans-serif
}
A {
	COLOR: #002bb8
}
A:visited {
	COLOR: #5a3696
}
A:active {
	COLOR: #ffa500
}
A.stub {
	COLOR: #772233
}
A.new {
	COLOR: #ba0000
}
#p-personal A.new {
	COLOR: #ba0000
}
A.new:visited {
	COLOR: #a55858
}
#p-personal A.new:visited {
	COLOR: #a55858
}
IMG {
	VERTICAL-ALIGN: middle; BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: =
none; BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: none
}
P {
	MARGIN: 0.4em 0em 0.5em; LINE-HEIGHT: 1.5em
}
P IMG {
	MARGIN: 0px
}
HR {
	BORDER-TOP-WIDTH: 0px; BORDER-LEFT-WIDTH: 0px; BORDER-BOTTOM-WIDTH: =
0px; MARGIN: 0.2em 0px; COLOR: #aaaaaa; HEIGHT: 1px; BACKGROUND-COLOR: =
#aaaaaa; BORDER-RIGHT-WIDTH: 0px
}
H1 {
	FONT-WEIGHT: normal; BACKGROUND: none transparent scroll repeat 0% 0%; =
PADDING-BOTTOM: 0.17em; MARGIN: 0px; COLOR: black; PADDING-TOP: 0.5em; =
BORDER-BOTTOM: #aaaaaa 1px solid
}
H2 {
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PADDING-BOTTOM: 0.17em; MARGIN: 0px; COLOR: black; PADDING-TOP: 0.5em; =
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}
H3 {
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PADDING-BOTTOM: 0.17em; MARGIN: 0px; COLOR: black; PADDING-TOP: 0.5em; =
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H4 {
	FONT-WEIGHT: normal; BACKGROUND: none transparent scroll repeat 0% 0%; =
PADDING-BOTTOM: 0.17em; MARGIN: 0px; COLOR: black; PADDING-TOP: 0.5em; =
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H5 {
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H6 {
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H1 .editsection {
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H3 {
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H4 {
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H5 {
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H6 {
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H5 {
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UL {
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0.3em 0px 0px 1.5em; LINE-HEIGHT: 1.5em; PADDING-TOP: 0px
}
OL {
	PADDING-RIGHT: 0px; PADDING-LEFT: 0px; LIST-STYLE-IMAGE: none; =
PADDING-BOTTOM: 0px; MARGIN: 0.3em 0px 0px 3.2em; LINE-HEIGHT: 1.5em; =
PADDING-TOP: 0px
}
LI {
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}
DT {
	FONT-WEIGHT: bold; MARGIN-BOTTOM: 0.1em
}
DL {
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}
DD {
	MARGIN-BOTTOM: 0.1em; MARGIN-LEFT: 2em; LINE-HEIGHT: 1.5em
}
FIELDSET {
	BORDER-RIGHT: #2f6fab 1px solid; PADDING-RIGHT: 1em; BORDER-TOP: =
#2f6fab 1px solid; PADDING-LEFT: 1em; PADDING-BOTTOM: 1em; MARGIN: 1em =
0em; BORDER-LEFT: #2f6fab 1px solid; LINE-HEIGHT: 1.5em; PADDING-TOP: =
0em; BORDER-BOTTOM: #2f6fab 1px solid
}
LEGEND {
	PADDING-RIGHT: 0.5em; PADDING-LEFT: 0.5em; FONT-SIZE: 95%; BACKGROUND: =
white; PADDING-BOTTOM: 0.5em; PADDING-TOP: 0.5em
}
FORM {
	MARGIN: 0px; BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; =
BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: none
}
TEXTAREA {
	BORDER-RIGHT: #2f6fab 1px solid; PADDING-RIGHT: 0.1em; BORDER-TOP: =
#2f6fab 1px solid; PADDING-LEFT: 0.1em; PADDING-BOTTOM: 0.1em; OVERFLOW: =
auto; BORDER-LEFT: #2f6fab 1px solid; WIDTH: 100%; COLOR: black; =
PADDING-TOP: 0.1em; BORDER-BOTTOM: #2f6fab 1px solid; BACKGROUND-COLOR: =
white
}

@media All   =20
{
HEAD:first-child + BODY INPUT {
	BORDER-RIGHT: #2f6fab 1px solid; PADDING-RIGHT: 0.2em; BORDER-TOP: =
#2f6fab 1px solid; PADDING-LEFT: 0.2em; VISIBILITY: visible; =
PADDING-BOTTOM: 0.2em; VERTICAL-ALIGN: middle; BORDER-LEFT: #2f6fab 1px =
solid; COLOR: black; PADDING-TOP: 0.2em; BORDER-BOTTOM: #2f6fab 1px =
solid; BACKGROUND-COLOR: white
}
    }
INPUT.historysubmit {
	PADDING-RIGHT: 0.3em! important; PADDING-LEFT: 0.3em! important; =
FONT-SIZE: 94%; PADDING-BOTTOM: 0.3em! important; MARGIN-LEFT: 1.6em; =
CURSOR: pointer; PADDING-TOP: 0px! important; HEIGHT: 1.7em! important
}
INPUT[type=3D'radio'] {
	BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; BORDER-LEFT-STYLE: =
none; BORDER-BOTTOM-STYLE: none
}
INPUT[type=3D'checkbox'] {
	BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; BORDER-LEFT-STYLE: =
none; BORDER-BOTTOM-STYLE: none
}
SELECT {
	BORDER-RIGHT: #2f6fab 1px solid; BORDER-TOP: #2f6fab 1px solid; =
VERTICAL-ALIGN: top; BORDER-LEFT: #2f6fab 1px solid; COLOR: black; =
BORDER-BOTTOM: #2f6fab 1px solid
}
ABBR {
	BACKGROUND: none transparent scroll repeat 0% 0%; CURSOR: help; COLOR: =
black; BORDER-BOTTOM: black 1px dotted
}
ACRONYM {
	BACKGROUND: none transparent scroll repeat 0% 0%; CURSOR: help; COLOR: =
black; BORDER-BOTTOM: black 1px dotted
}
.explain {
	BACKGROUND: none transparent scroll repeat 0% 0%; CURSOR: help; COLOR: =
black; BORDER-BOTTOM: black 1px dotted
}
Q {
	FONT-STYLE: italic; FONT-FAMILY: Times, "Times New Roman", serif
}
CODE {
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}
PRE {
	BORDER-RIGHT: #2f6fab 1px dashed; PADDING-RIGHT: 1em; BORDER-TOP: =
#2f6fab 1px dashed; PADDING-LEFT: 1em; PADDING-BOTTOM: 1em; BORDER-LEFT: =
#2f6fab 1px dashed; COLOR: black; LINE-HEIGHT: 1.1em; PADDING-TOP: 1em; =
BORDER-BOTTOM: #2f6fab 1px dashed; BACKGROUND-COLOR: #f9f9f9
}
SPAN.subpages {
	DISPLAY: block
}
#bodyContent H1 {
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}
#bodyContent H2 {
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}
#bodyContent H3 {
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}
#bodyContent H4 {
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}
#bodyContent H5 {
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}
#firstHeading {
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}
.usermessage {
	BORDER-RIGHT: #ffa500 1px solid; PADDING-RIGHT: 5px; BORDER-TOP: =
#ffa500 1px solid; PADDING-LEFT: 5px; FONT-WEIGHT: bold; PADDING-BOTTOM: =
2px; MARGIN: 0.1em 0px 0px; VERTICAL-ALIGN: middle; BORDER-LEFT: #ffa500 =
1px solid; COLOR: black; PADDING-TOP: 2px; BORDER-BOTTOM: #ffa500 1px =
solid; BACKGROUND-COLOR: #ffce7b
}
#siteNotice {
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PADDING-BOTTOM: 0px; PADDING-TOP: 0px; TEXT-ALIGN: center
}
#siteNotice P {
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0px; PADDING-TOP: 0px
}
.error {
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}
.catlinks {
	CLEAR: both; BORDER-RIGHT: #aaaaaa 1px solid; PADDING-RIGHT: 5px; =
BORDER-TOP: #aaaaaa 1px solid; PADDING-LEFT: 5px; PADDING-BOTTOM: 2px; =
MARGIN: 0.1em 0px 0px; BORDER-LEFT: #aaaaaa 1px solid; PADDING-TOP: 2px; =
BORDER-BOTTOM: #aaaaaa 1px solid; BACKGROUND-COLOR: #f9f9f9
}
.catlinks {
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0px; PADDING-TOP: 0px
}
.documentDescription {
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}
.documentByLine {
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TEXT-ALIGN: right
}
.center {
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}
*.center * {
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}
.small {
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}
.small * {
	FONT-SIZE: 94%
}
TABLE.small {
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}
#toc {
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#aaaaaa 1px solid; PADDING-LEFT: 5px; FONT-SIZE: 95%; PADDING-BOTTOM: =
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}
#toc UL {
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}
#toc .toctoggle {
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}
#toc .editsection {
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}
DIV.floatright {
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}
TABLE.floatright {
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DIV.floatright P {
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}
DIV.floatleft {
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}
TABLE.floatleft {
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}
DIV.floatleft P {
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}
DIV.thumb {
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white; WIDTH: auto; BORDER-TOP-STYLE: solid; BORDER-TOP-COLOR: white; =
BORDER-RIGHT-STYLE: solid; BORDER-LEFT-STYLE: solid; BORDER-RIGHT-COLOR: =
white; BORDER-BOTTOM-STYLE: solid
}
DIV.thumb DIV {
	BORDER-RIGHT: #cccccc 1px solid; PADDING-RIGHT: 3px! important; =
BORDER-TOP: #cccccc 1px solid; PADDING-LEFT: 3px! important; FONT-SIZE: =
94%; PADDING-BOTTOM: 3px! important; OVERFLOW: hidden; BORDER-LEFT: =
#cccccc 1px solid; PADDING-TOP: 3px! important; BORDER-BOTTOM: #cccccc =
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}
DIV.thumb DIV A IMG {
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BORDER-LEFT: #cccccc 1px solid; BORDER-BOTTOM: #cccccc 1px solid
}
DIV.thumb DIV DIV.thumbcaption {
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BORDER-RIGHT-STYLE: none; BORDER-LEFT-STYLE: none; TEXT-ALIGN: left; =
BORDER-BOTTOM-STYLE: none
}
DIV.magnify {
	BACKGROUND: none transparent scroll repeat 0% 0%; FLOAT: right; =
BORDER-TOP-STYLE: none! important; BORDER-RIGHT-STYLE: none! important; =
BORDER-LEFT-STYLE: none! important; BORDER-BOTTOM-STYLE: none! important
}
DIV.magnify A {
	DISPLAY: block; BACKGROUND: none transparent scroll repeat 0% 0%; =
BORDER-TOP-STYLE: none! important; BORDER-RIGHT-STYLE: none! important; =
BORDER-LEFT-STYLE: none! important; BORDER-BOTTOM-STYLE: none! important
}
DIV.magnify IMG {
	DISPLAY: block; BACKGROUND: none transparent scroll repeat 0% 0%; =
BORDER-TOP-STYLE: none! important; BORDER-RIGHT-STYLE: none! important; =
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}
DIV.tright {
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right; BORDER-BOTTOM-WIDTH: 0.8em; BORDER-RIGHT-WIDTH: 0px
}
DIV.tleft {
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left; BORDER-BOTTOM-WIDTH: 0.8em; MARGIN-RIGHT: 0.5em; =
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}
IMG.thumbborder {
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BORDER-LEFT: #dddddd 1px solid; BORDER-BOTTOM: #dddddd 1px solid
}
.hiddenStructure {
	DISPLAY: none
}
TABLE.rimage {
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TEXT-ALIGN: center
}
.toccolours {
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#aaaaaa 1px solid; PADDING-LEFT: 5px; FONT-SIZE: 95%; PADDING-BOTTOM: =
5px; BORDER-LEFT: #aaaaaa 1px solid; PADDING-TOP: 5px; BORDER-BOTTOM: =
#aaaaaa 1px solid; BACKGROUND-COLOR: #f9f9f9
}
.special LI {
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0px; LINE-HEIGHT: 1.4em; PADDING-TOP: 0px
}
A.external {
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}
DIV#footer {
	TEXT-ALIGN: center
}
UL#f-list LI {
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}
DIV.portlet {
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/**=0A=
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/**=0A=
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 * @param String id -- id of the new item, should be unique and =
preferably have the appropriate prefix ("ca-", "pt-", "n-" or "t-")=0A=
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 * @param String accesskey -- accesskey to activate this link (one =
character, try to avoid conflicts)=0A=
 * @param Node nextnode -- the DOM node before which the new item should =
be added, should be another item in the same list=0A=
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 * @return Node -- the DOM node of the new item (an LI element) or null=0A=
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function addPortletLink(portlet, href, text, id, tooltip, accesskey, =
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function getInnerText(el) {=0A=
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faster=0A=
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/**=0A=
 * Set up accesskeys/tooltips from the deprecated ta array.  If doId=0A=
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 */=0A=
function akeytt( doId ) {=0A=
	// A lot of user scripts (and some of the code below) break if=0A=
	// ta isn't defined, so we make sure it is.  Explictly using=0A=
	// window.ta avoids a "ta is not defined" error.=0A=
	if (!window.ta) window.ta =3D new Array;=0A=
=0A=
	// Make a local, possibly restricted, copy to avoid clobbering=0A=
	// the original.=0A=
	var ta;=0A=
	if ( doId ) {=0A=
		ta =3D [doId];=0A=
	} else {=0A=
		ta =3D window.ta;=0A=
	}=0A=
=0A=
	// Now deal with evil deprecated ta=0A=
	var watchCheckboxExists =3D document.getElementById( 'wpWatchthis' ) ? =
true : false;=0A=
	for (var id in ta) {=0A=
		var n =3D document.getElementById(id);=0A=
		if (n) {=0A=
			var a =3D null;=0A=
			var ak =3D '';=0A=
			// Are we putting accesskey in it=0A=
			if (ta[id][0].length > 0) {=0A=
				// Is this object a object? If not assume it's the next child.=0A=
=0A=
				if (n.nodeName.toLowerCase() =3D=3D "a") {=0A=
					a =3D n;=0A=
				} else {=0A=
					a =3D n.childNodes[0];=0A=
				}=0A=
			 	// Don't add an accesskey for the watch tab if the watch=0A=
			 	// checkbox is also available.=0A=
				if (a && ((id !=3D 'ca-watch' && id !=3D 'ca-unwatch') || =
!watchCheckboxExists)) {=0A=
					a.accessKey =3D ta[id][0];=0A=
					ak =3D ' ['+tooltipAccessKeyPrefix+ta[id][0]+']';=0A=
				}=0A=
			} else {=0A=
				// We don't care what type the object is when assigning tooltip=0A=
				a =3D n;=0A=
				ak =3D '';=0A=
			}=0A=
=0A=
			if (a) {=0A=
				a.title =3D ta[id][1]+ak;=0A=
			}=0A=
		}=0A=
	}=0A=
}=0A=
=0A=
var checkboxes;=0A=
var lastCheckbox;=0A=
=0A=
function setupCheckboxShiftClick() {=0A=
	checkboxes =3D [];=0A=
	lastCheckbox =3D null;=0A=
	var inputs =3D document.getElementsByTagName('input');=0A=
	addCheckboxClickHandlers(inputs);=0A=
}=0A=
=0A=
function addCheckboxClickHandlers(inputs, start) {=0A=
	if ( !start) start =3D 0;=0A=
=0A=
	var finish =3D start + 250;=0A=
	if ( finish > inputs.length )=0A=
		finish =3D inputs.length;=0A=
=0A=
	for ( var i =3D start; i < finish; i++ ) {=0A=
		var cb =3D inputs[i];=0A=
		if ( !cb.type || cb.type.toLowerCase() !=3D 'checkbox' )=0A=
			continue;=0A=
		var end =3D checkboxes.length;=0A=
		checkboxes[end] =3D cb;=0A=
		cb.index =3D end;=0A=
		cb.onclick =3D checkboxClickHandler;=0A=
	}=0A=
=0A=
	if ( finish < inputs.length ) {=0A=
		setTimeout( function () {=0A=
			addCheckboxClickHandlers(inputs, finish);=0A=
		}, 200 );=0A=
	}=0A=
}=0A=
=0A=
function checkboxClickHandler(e) {=0A=
	if (typeof e =3D=3D 'undefined') {=0A=
		e =3D window.event;=0A=
	}=0A=
	if ( !e.shiftKey || lastCheckbox =3D=3D=3D null ) {=0A=
		lastCheckbox =3D this.index;=0A=
		return true;=0A=
	}=0A=
	var endState =3D this.checked;=0A=
	var start, finish;=0A=
	if ( this.index < lastCheckbox ) {=0A=
		start =3D this.index + 1;=0A=
		finish =3D lastCheckbox;=0A=
	} else {=0A=
		start =3D lastCheckbox;=0A=
		finish =3D this.index - 1;=0A=
	}=0A=
	for (var i =3D start; i <=3D finish; ++i ) {=0A=
		checkboxes[i].checked =3D endState;=0A=
		if( i > start && typeof checkboxes[i].onchange =3D=3D 'function' )=0A=
			checkboxes[i].onchange(); // fire triggers=0A=
	}=0A=
	lastCheckbox =3D this.index;=0A=
	return true;=0A=
}=0A=
=0A=
function toggle_element_activation(ida,idb) {=0A=
	if (!document.getElementById) {=0A=
		return;=0A=
	}=0A=
	document.getElementById(ida).disabled=3Dtrue;=0A=
	document.getElementById(idb).disabled=3Dfalse;=0A=
}=0A=
=0A=
function toggle_element_check(ida,idb) {=0A=
	if (!document.getElementById) {=0A=
		return;=0A=
	}=0A=
	document.getElementById(ida).checked=3Dtrue;=0A=
	document.getElementById(idb).checked=3Dfalse;=0A=
}=0A=
=0A=
/*=0A=
	Written by Jonathan Snook, http://www.snook.ca/jonathan=0A=
	Add-ons by Robert Nyman, http://www.robertnyman.com=0A=
	Author says "The credit comment is all it takes, no license. Go crazy =
with it!:-)"=0A=
	From =
http://www.robertnyman.com/2005/11/07/the-ultimate-getelementsbyclassname=
/=0A=
*/=0A=
function getElementsByClassName(oElm, strTagName, oClassNames){=0A=
	var arrReturnElements =3D new Array();=0A=
	if ( typeof( oElm.getElementsByClassName ) =3D=3D "function" ) {=0A=
		/* Use a native implementation where possible FF3, Saf3.2, Opera 9.5 */=0A=
		var arrNativeReturn =3D oElm.getElementsByClassName( oClassNames );=0A=
		if ( strTagName =3D=3D "*" )=0A=
			return arrNativeReturn;=0A=
		for ( var h=3D0; h < arrNativeReturn.length; h++ ) {=0A=
			if( arrNativeReturn[h].tagName.toLowerCase() =3D=3D =
strTagName.toLowerCase() )=0A=
				arrReturnElements[arrReturnElements.length] =3D arrNativeReturn[h];=0A=
		}=0A=
		return arrReturnElements;=0A=
	}=0A=
	var arrElements =3D (strTagName =3D=3D "*" && oElm.all)? oElm.all : =
oElm.getElementsByTagName(strTagName);=0A=
	var arrRegExpClassNames =3D new Array();=0A=
	if(typeof oClassNames =3D=3D "object"){=0A=
		for(var i=3D0; i<oClassNames.length; i++){=0A=
			arrRegExpClassNames[arrRegExpClassNames.length] =3D=0A=
				new RegExp("(^|\\s)" + oClassNames[i].replace(/\-/g, "\\-") + =
"(\\s|$)");=0A=
		}=0A=
	}=0A=
	else{=0A=
		arrRegExpClassNames[arrRegExpClassNames.length] =3D=0A=
			new RegExp("(^|\\s)" + oClassNames.replace(/\-/g, "\\-") + "(\\s|$)");=0A=
	}=0A=
	var oElement;=0A=
	var bMatchesAll;=0A=
	for(var j=3D0; j<arrElements.length; j++){=0A=
		oElement =3D arrElements[j];=0A=
		bMatchesAll =3D true;=0A=
		for(var k=3D0; k<arrRegExpClassNames.length; k++){=0A=
			if(!arrRegExpClassNames[k].test(oElement.className)){=0A=
				bMatchesAll =3D false;=0A=
				break;=0A=
			}=0A=
		}=0A=
		if(bMatchesAll){=0A=
			arrReturnElements[arrReturnElements.length] =3D oElement;=0A=
		}=0A=
	}=0A=
	return (arrReturnElements)=0A=
}=0A=
=0A=
function redirectToFragment(fragment) {=0A=
	var match =3D navigator.userAgent.match(/AppleWebKit\/(\d+)/);=0A=
	if (match) {=0A=
		var webKitVersion =3D parseInt(match[1]);=0A=
		if (webKitVersion < 420) {=0A=
			// Released Safari w/ WebKit 418.9.1 messes up horribly=0A=
			// Nightlies of 420+ are ok=0A=
			return;=0A=
		}=0A=
	}=0A=
	if (is_gecko) {=0A=
		// Mozilla needs to wait until after load, otherwise the window =
doesn't scroll=0A=
		addOnloadHook(function () {=0A=
			if (window.location.hash =3D=3D "")=0A=
				window.location.hash =3D fragment;=0A=
		});=0A=
	} else {=0A=
		if (window.location.hash =3D=3D "")=0A=
			window.location.hash =3D fragment;=0A=
	}=0A=
}=0A=
=0A=
/*=0A=
 * Table sorting script based on one (c) 1997-2006 Stuart Langridge and =
Joost=0A=
 * de Valk:=0A=
 * http://www.joostdevalk.nl/code/sortable-table/=0A=
 * http://www.kryogenix.org/code/browser/sorttable/=0A=
 *=0A=
 * @todo don't break on colspans/rowspans (bug 8028)=0A=
 * @todo language-specific digit grouping/decimals (bug 8063)=0A=
 * @todo support all accepted date formats (bug 8226)=0A=
 */=0A=
=0A=
var ts_image_path =3D stylepath+"/common/images/";=0A=
var ts_image_up =3D "sort_up.gif";=0A=
var ts_image_down =3D "sort_down.gif";=0A=
var ts_image_none =3D "sort_none.gif";=0A=
var ts_europeandate =3D wgContentLanguage !=3D "en"; // The =
non-American-inclined can change to "true"=0A=
var ts_alternate_row_colors =3D false;=0A=
var ts_number_transform_table =3D null;=0A=
var ts_number_regex =3D null;=0A=
=0A=
function sortables_init() {=0A=
	var idnum =3D 0;=0A=
	// Find all tables with class sortable and make them sortable=0A=
	var tables =3D getElementsByClassName(document, "table", "sortable");=0A=
	for (var ti =3D 0; ti < tables.length ; ti++) {=0A=
		if (!tables[ti].id) {=0A=
			tables[ti].setAttribute('id','sortable_table_id_'+idnum);=0A=
			++idnum;=0A=
		}=0A=
		ts_makeSortable(tables[ti]);=0A=
	}=0A=
}=0A=
=0A=
function ts_makeSortable(table) {=0A=
	var firstRow;=0A=
	if (table.rows && table.rows.length > 0) {=0A=
		if (table.tHead && table.tHead.rows.length > 0) {=0A=
			firstRow =3D table.tHead.rows[table.tHead.rows.length-1];=0A=
		} else {=0A=
			firstRow =3D table.rows[0];=0A=
		}=0A=
	}=0A=
	if (!firstRow) return;=0A=
=0A=
	// We have a first row: assume it's the header, and make its contents =
clickable links=0A=
	for (var i =3D 0; i < firstRow.cells.length; i++) {=0A=
		var cell =3D firstRow.cells[i];=0A=
		if ((" "+cell.className+" ").indexOf(" unsortable ") =3D=3D -1) {=0A=
			cell.innerHTML +=3D '&nbsp;&nbsp;'=0A=
				+ '<a href=3D"#" class=3D"sortheader" '=0A=
				+ 'onclick=3D"ts_resortTable(this);return false;">'=0A=
				+ '<span class=3D"sortarrow">'=0A=
				+ '<img src=3D"'=0A=
				+ ts_image_path=0A=
				+ ts_image_none=0A=
				+ '" alt=3D"&darr;"/></span></a>';=0A=
		}=0A=
	}=0A=
	if (ts_alternate_row_colors) {=0A=
		ts_alternate(table);=0A=
	}=0A=
}=0A=
=0A=
function ts_getInnerText(el) {=0A=
	return getInnerText( el );=0A=
}=0A=
=0A=
function ts_resortTable(lnk) {=0A=
	// get the span=0A=
	var span =3D lnk.getElementsByTagName('span')[0];=0A=
=0A=
	var td =3D lnk.parentNode;=0A=
	var tr =3D td.parentNode;=0A=
	var column =3D td.cellIndex;=0A=
=0A=
	var table =3D tr.parentNode;=0A=
	while (table && !(table.tagName && table.tagName.toLowerCase() =3D=3D =
'table'))=0A=
		table =3D table.parentNode;=0A=
	if (!table) return;=0A=
=0A=
	if (table.rows.length <=3D 1) return;=0A=
=0A=
	// Generate the number transform table if it's not done already=0A=
	if (ts_number_transform_table =3D=3D null) {=0A=
		ts_initTransformTable();=0A=
	}=0A=
=0A=
	// Work out a type for the column=0A=
	// Skip the first row if that's where the headings are=0A=
	var rowStart =3D (table.tHead && table.tHead.rows.length > 0 ? 0 : 1);=0A=
=0A=
	var itm =3D "";=0A=
	for (var i =3D rowStart; i < table.rows.length; i++) {=0A=
		if (table.rows[i].cells.length > column) {=0A=
			itm =3D ts_getInnerText(table.rows[i].cells[column]);=0A=
			itm =3D itm.replace(/^[\s\xa0]+/, "").replace(/[\s\xa0]+$/, "");=0A=
			if (itm !=3D "") break;=0A=
		}=0A=
	}=0A=
=0A=
	// TODO: bug 8226, localised date formats=0A=
	var sortfn =3D ts_sort_generic;=0A=
	var preprocessor =3D ts_toLowerCase;=0A=
	if (/^\d\d[\/. -][a-zA-Z]{3}[\/. -]\d\d\d\d$/.test(itm)) {=0A=
		preprocessor =3D ts_dateToSortKey;=0A=
	} else if (/^\d\d[\/.-]\d\d[\/.-]\d\d\d\d$/.test(itm)) {=0A=
		preprocessor =3D ts_dateToSortKey;=0A=
	} else if (/^\d\d[\/.-]\d\d[\/.-]\d\d$/.test(itm)) {=0A=
		preprocessor =3D ts_dateToSortKey;=0A=
	// pound dollar euro yen currency cents=0A=
	} else if (/(^[\u00a3$\u20ac\u00a4\u00a5]|\u00a2$)/.test(itm)) {=0A=
		preprocessor =3D ts_currencyToSortKey;=0A=
	} else if (ts_number_regex.test(itm)) {=0A=
		preprocessor =3D ts_parseFloat;=0A=
	}=0A=
=0A=
	var reverse =3D (span.getAttribute("sortdir") =3D=3D 'down');=0A=
=0A=
	var newRows =3D new Array();=0A=
	var staticRows =3D new Array();=0A=
	for (var j =3D rowStart; j < table.rows.length; j++) {=0A=
		var row =3D table.rows[j];=0A=
		if((" "+row.className+" ").indexOf(" unsortable ") < 0) {=0A=
			var keyText =3D ts_getInnerText(row.cells[column]);=0A=
			var oldIndex =3D (reverse ? -j : j);=0A=
			var preprocessed =3D preprocessor( keyText );=0A=
=0A=
			newRows[newRows.length] =3D new Array(row, preprocessed, oldIndex);=0A=
		} else staticRows[staticRows.length] =3D new Array(row, false, =
j-rowStart);=0A=
	}=0A=
=0A=
	newRows.sort(sortfn);=0A=
=0A=
	var arrowHTML;=0A=
	if (reverse) {=0A=
		arrowHTML =3D '<img src=3D"'+ ts_image_path + ts_image_down + '" =
alt=3D"&darr;"/>';=0A=
		newRows.reverse();=0A=
		span.setAttribute('sortdir','up');=0A=
	} else {=0A=
		arrowHTML =3D '<img src=3D"'+ ts_image_path + ts_image_up + '" =
alt=3D"&uarr;"/>';=0A=
		span.setAttribute('sortdir','down');=0A=
	}=0A=
=0A=
	for (var i =3D 0; i < staticRows.length; i++) {=0A=
		var row =3D staticRows[i];=0A=
		newRows.splice(row[2], 0, row);=0A=
	}=0A=
=0A=
	// We appendChild rows that already exist to the tbody, so it moves =
them rather than creating new ones=0A=
	// don't do sortbottom rows=0A=
	for (var i =3D 0; i < newRows.length; i++) {=0A=
		if ((" "+newRows[i][0].className+" ").indexOf(" sortbottom ") =3D=3D =
-1)=0A=
			table.tBodies[0].appendChild(newRows[i][0]);=0A=
	}=0A=
	// do sortbottom rows only=0A=
	for (var i =3D 0; i < newRows.length; i++) {=0A=
		if ((" "+newRows[i][0].className+" ").indexOf(" sortbottom ") !=3D -1)=0A=
			table.tBodies[0].appendChild(newRows[i][0]);=0A=
	}=0A=
=0A=
	// Delete any other arrows there may be showing=0A=
	var spans =3D getElementsByClassName(tr, "span", "sortarrow");=0A=
	for (var i =3D 0; i < spans.length; i++) {=0A=
		spans[i].innerHTML =3D '<img src=3D"'+ ts_image_path + ts_image_none + =
'" alt=3D"&darr;"/>';=0A=
	}=0A=
	span.innerHTML =3D arrowHTML;=0A=
=0A=
	if (ts_alternate_row_colors) {=0A=
		ts_alternate(table);=0A=
	}=0A=
}=0A=
=0A=
function ts_initTransformTable() {=0A=
	if ( typeof wgSeparatorTransformTable =3D=3D "undefined"=0A=
			|| ( wgSeparatorTransformTable[0] =3D=3D '' && =
wgDigitTransformTable[2] =3D=3D '' ) )=0A=
	{=0A=
		digitClass =3D "[0-9,.]";=0A=
		ts_number_transform_table =3D false;=0A=
	} else {=0A=
		ts_number_transform_table =3D {};=0A=
		// Unpack the transform table=0A=
		// Separators=0A=
		ascii =3D wgSeparatorTransformTable[0].split("\t");=0A=
		localised =3D wgSeparatorTransformTable[1].split("\t");=0A=
		for ( var i =3D 0; i < ascii.length; i++ ) { =0A=
			ts_number_transform_table[localised[i]] =3D ascii[i];=0A=
		}=0A=
		// Digits=0A=
		ascii =3D wgDigitTransformTable[0].split("\t");=0A=
		localised =3D wgDigitTransformTable[1].split("\t");=0A=
		for ( var i =3D 0; i < ascii.length; i++ ) { =0A=
			ts_number_transform_table[localised[i]] =3D ascii[i];=0A=
		}=0A=
=0A=
		// Construct regex for number identification=0A=
		digits =3D ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', ',', =
'\\.'];=0A=
		maxDigitLength =3D 1;=0A=
		for ( var digit in ts_number_transform_table ) {=0A=
			// Escape regex metacharacters=0A=
			digits.push( =0A=
				digit.replace( /[\\\\$\*\+\?\.\(\)\|\{\}\[\]\-]/,=0A=
					function( s ) { return '\\' + s; } )=0A=
			);=0A=
			if (digit.length > maxDigitLength) {=0A=
				maxDigitLength =3D digit.length;=0A=
			}=0A=
		}=0A=
		if ( maxDigitLength > 1 ) {=0A=
			digitClass =3D '[' + digits.join( '', digits ) + ']';=0A=
		} else {=0A=
			digitClass =3D '(' + digits.join( '|', digits ) + ')';=0A=
		}=0A=
	}=0A=
=0A=
	// We allow a trailing percent sign, which we just strip.  This works =
fine=0A=
	// if percents and regular numbers aren't being mixed.=0A=
	ts_number_regex =3D new RegExp(=0A=
		"^(" +=0A=
			"[+-]?[0-9][0-9,]*(\\.[0-9,]*)?(E[+-]?[0-9][0-9,]*)?" + // =
Fortran-style scientific=0A=
			"|" +=0A=
			"[+-]?" + digitClass + "+%?" + // Generic localised=0A=
		")$", "i"=0A=
	);=0A=
}=0A=
=0A=
function ts_toLowerCase( s ) {=0A=
	return s.toLowerCase();=0A=
}=0A=
=0A=
function ts_dateToSortKey(date) {	=0A=
	// y2k notes: two digit years less than 50 are treated as 20XX, greater =
than 50 are treated as 19XX=0A=
	if (date.length =3D=3D 11) {=0A=
		switch (date.substr(3,3).toLowerCase()) {=0A=
			case "jan": var month =3D "01"; break;=0A=
			case "feb": var month =3D "02"; break;=0A=
			case "mar": var month =3D "03"; break;=0A=
			case "apr": var month =3D "04"; break;=0A=
			case "may": var month =3D "05"; break;=0A=
			case "jun": var month =3D "06"; break;=0A=
			case "jul": var month =3D "07"; break;=0A=
			case "aug": var month =3D "08"; break;=0A=
			case "sep": var month =3D "09"; break;=0A=
			case "oct": var month =3D "10"; break;=0A=
			case "nov": var month =3D "11"; break;=0A=
			case "dec": var month =3D "12"; break;=0A=
			// default: var month =3D "00";=0A=
		}=0A=
		return date.substr(7,4)+month+date.substr(0,2);=0A=
	} else if (date.length =3D=3D 10) {=0A=
		if (ts_europeandate =3D=3D false) {=0A=
			return date.substr(6,4)+date.substr(0,2)+date.substr(3,2);=0A=
		} else {=0A=
			return date.substr(6,4)+date.substr(3,2)+date.substr(0,2);=0A=
		}=0A=
	} else if (date.length =3D=3D 8) {=0A=
		yr =3D date.substr(6,2);=0A=
		if (parseInt(yr) < 50) { =0A=
			yr =3D '20'+yr; =0A=
		} else { =0A=
			yr =3D '19'+yr; =0A=
		}=0A=
		if (ts_europeandate =3D=3D true) {=0A=
			return yr+date.substr(3,2)+date.substr(0,2);=0A=
		} else {=0A=
			return yr+date.substr(0,2)+date.substr(3,2);=0A=
		}=0A=
	}=0A=
	return "00000000";=0A=
}=0A=
=0A=
function ts_parseFloat( s ) {=0A=
	if ( !s ) {=0A=
		return 0;=0A=
	}=0A=
	if (ts_number_transform_table !=3D false) {=0A=
		var newNum =3D '', c;=0A=
		=0A=
		for ( var p =3D 0; p < s.length; p++ ) {=0A=
			c =3D s.charAt( p );=0A=
			if (c in ts_number_transform_table) {=0A=
				newNum +=3D ts_number_transform_table[c];=0A=
			} else {=0A=
				newNum +=3D c;=0A=
			}=0A=
		}=0A=
		s =3D newNum;=0A=
	}=0A=
=0A=
	num =3D parseFloat(s.replace(/,/g, ""));=0A=
	return (isNaN(num) ? 0 : num);=0A=
}=0A=
=0A=
function ts_currencyToSortKey( s ) {=0A=
	return ts_parseFloat(s.replace(/[^0-9.,]/g,''));=0A=
}=0A=
=0A=
function ts_sort_generic(a, b) {=0A=
	return a[1] < b[1] ? -1 : a[1] > b[1] ? 1 : a[2] - b[2];=0A=
}=0A=
=0A=
function ts_alternate(table) {=0A=
	// Take object table and get all it's tbodies.=0A=
	var tableBodies =3D table.getElementsByTagName("tbody");=0A=
	// Loop through these tbodies=0A=
	for (var i =3D 0; i < tableBodies.length; i++) {=0A=
		// Take the tbody, and get all it's rows=0A=
		var tableRows =3D tableBodies[i].getElementsByTagName("tr");=0A=
		// Loop through these rows=0A=
		// Start at 1 because we want to leave the heading row untouched=0A=
		for (var j =3D 0; j < tableRows.length; j++) {=0A=
			// Check if j is even, and apply classes for both possible results=0A=
			var oldClasses =3D tableRows[j].className.split(" ");=0A=
			var newClassName =3D "";=0A=
			for (var k =3D 0; k < oldClasses.length; k++) {=0A=
				if (oldClasses[k] !=3D "" && oldClasses[k] !=3D "even" && =
oldClasses[k] !=3D "odd")=0A=
					newClassName +=3D oldClasses[k] + " ";=0A=
			}=0A=
			tableRows[j].className =3D newClassName + (j % 2 =3D=3D 0 ? "even" : =
"odd");=0A=
		}=0A=
	}=0A=
}=0A=
=0A=
/*=0A=
 * End of table sorting code=0A=
 */=0A=
 =0A=
 =0A=
/**=0A=
 * Add a cute little box at the top of the screen to inform the user of=0A=
 * something, replacing any preexisting message.=0A=
 *=0A=
 * @param String -or- Dom Object message HTML to be put inside the right =
div=0A=
 * @param String className   Used in adding a class; should be different =
for each=0A=
 *   call to allow CSS/JS to hide different boxes.  null =3D no class =
used.=0A=
 * @return Boolean       True on success, false on failure=0A=
 */=0A=
function jsMsg( message, className ) {=0A=
	if ( !document.getElementById ) {=0A=
		return false;=0A=
	}=0A=
	// We special-case skin structures provided by the software.  Skins that=0A=
	// choose to abandon or significantly modify our formatting can just =
define=0A=
	// an mw-js-message div to start with.=0A=
	var messageDiv =3D document.getElementById( 'mw-js-message' );=0A=
	if ( !messageDiv ) {=0A=
		messageDiv =3D document.createElement( 'div' );=0A=
		if ( document.getElementById( 'column-content' )=0A=
		&& document.getElementById( 'content' ) ) {=0A=
			// MonoBook, presumably=0A=
			document.getElementById( 'content' ).insertBefore(=0A=
				messageDiv,=0A=
				document.getElementById( 'content' ).firstChild=0A=
			);=0A=
		} else if ( document.getElementById('content')=0A=
		&& document.getElementById( 'article' ) ) {=0A=
			// Non-Monobook but still recognizable (old-style)=0A=
			document.getElementById( 'article').insertBefore(=0A=
				messageDiv,=0A=
				document.getElementById( 'article' ).firstChild=0A=
			);=0A=
		} else {=0A=
			return false;=0A=
		}=0A=
	}=0A=
=0A=
	messageDiv.setAttribute( 'id', 'mw-js-message' );=0A=
	messageDiv.style.display =3D 'block';=0A=
	if( className ) {=0A=
		messageDiv.setAttribute( 'class', 'mw-js-message-'+className );=0A=
	}=0A=
	=0A=
	if (typeof message =3D=3D=3D 'object') {=0A=
		while (messageDiv.hasChildNodes()) // Remove old content=0A=
			messageDiv.removeChild(messageDiv.firstChild);=0A=
		messageDiv.appendChild (message); // Append new content=0A=
	}=0A=
	else {=0A=
		messageDiv.innerHTML =3D message;=0A=
	}=0A=
	return true;=0A=
}=0A=
=0A=
/**=0A=
 * Inject a cute little progress spinner after the specified element=0A=
 *=0A=
 * @param element Element to inject after=0A=
 * @param id Identifier string (for use with removeSpinner(), below)=0A=
 */=0A=
function injectSpinner( element, id ) {=0A=
	var spinner =3D document.createElement( "img" );=0A=
	spinner.id =3D "mw-spinner-" + id;=0A=
	spinner.src =3D stylepath + "/common/images/spinner.gif";=0A=
	spinner.alt =3D spinner.title =3D "...";=0A=
	if( element.nextSibling ) {=0A=
		element.parentNode.insertBefore( spinner, element.nextSibling );=0A=
	} else {=0A=
		element.parentNode.appendChild( spinner );=0A=
	}=0A=
}=0A=
=0A=
/**=0A=
 * Remove a progress spinner added with injectSpinner()=0A=
 *=0A=
 * @param id Identifier string=0A=
 */=0A=
function removeSpinner( id ) {=0A=
	var spinner =3D document.getElementById( "mw-spinner-" + id );=0A=
	if( spinner ) {=0A=
		spinner.parentNode.removeChild( spinner );=0A=
	}=0A=
}=0A=
=0A=
function runOnloadHook() {=0A=
	// don't run anything below this for non-dom browsers=0A=
	if (doneOnloadHook || !(document.getElementById && =
document.getElementsByTagName)) {=0A=
		return;=0A=
	}=0A=
=0A=
	// set this before running any hooks, since any errors below=0A=
	// might cause the function to terminate prematurely=0A=
	doneOnloadHook =3D true;=0A=
=0A=
	updateTooltipAccessKeys( null );=0A=
	akeytt( null );=0A=
	setupCheckboxShiftClick();=0A=
	sortables_init();=0A=
=0A=
	// Run any added-on functions=0A=
	for (var i =3D 0; i < onloadFuncts.length; i++) {=0A=
		onloadFuncts[i]();=0A=
	}=0A=
}=0A=
=0A=
/**=0A=
 * Add an event handler to an element=0A=
 *=0A=
 * @param Element element Element to add handler to=0A=
 * @param String attach Event to attach to=0A=
 * @param callable handler Event handler callback=0A=
 */=0A=
function addHandler( element, attach, handler ) {=0A=
	if( window.addEventListener ) {=0A=
		element.addEventListener( attach, handler, false );=0A=
	} else if( window.attachEvent ) {=0A=
		element.attachEvent( 'on' + attach, handler );=0A=
	}=0A=
}=0A=
=0A=
/**=0A=
 * Add a click event handler to an element=0A=
 *=0A=
 * @param Element element Element to add handler to=0A=
 * @param callable handler Event handler callback=0A=
 */=0A=
function addClickHandler( element, handler ) {=0A=
	addHandler( element, 'click', handler );=0A=
}=0A=
=0A=
/**=0A=
 * Removes an event handler from an element=0A=
 *=0A=
 * @param Element element Element to remove handler from=0A=
 * @param String remove Event to remove=0A=
 * @param callable handler Event handler callback to remove=0A=
 */=0A=
function removeHandler( element, remove, handler ) {=0A=
	if( window.removeEventListener ) {=0A=
		element.removeEventListener( remove, handler, false );=0A=
	} else if( window.detachEvent ) {=0A=
		element.detachEvent( 'on' + remove, handler );=0A=
	}=0A=
}=0A=
//note: all skins should call runOnloadHook() at the end of html output,=0A=
//      so the below should be redundant. It's there just in case.=0A=
hookEvent("load", runOnloadHook);=0A=

------=_NextPart_000_0049_01CA353D.AD380F90
Content-Type: application/octet-stream
Content-Transfer-Encoding: quoted-printable
Content-Location: http://en.wikipedia.org/skins-1.5/common/ajax.js?233zz2

// remote scripting library=0A=
// (c) copyright 2005 modernmethod, inc=0A=
var sajax_debug_mode =3D false;=0A=
var sajax_request_type =3D "GET";=0A=
=0A=
/**=0A=
* if sajax_debug_mode is true, this function outputs given the message =
into =0A=
* the element with id =3D sajax_debug; if no such element exists in the =
document, =0A=
* it is injected.=0A=
*/=0A=
function sajax_debug(text) {=0A=
	if (!sajax_debug_mode) return false;=0A=
=0A=
	var e=3D document.getElementById('sajax_debug');=0A=
=0A=
	if (!e) {=0A=
		e=3D document.createElement("p");=0A=
		e.className=3D 'sajax_debug';=0A=
		e.id=3D 'sajax_debug';=0A=
=0A=
		var b=3D document.getElementsByTagName("body")[0];=0A=
=0A=
		if (b.firstChild) b.insertBefore(e, b.firstChild);=0A=
		else b.appendChild(e);=0A=
	}=0A=
=0A=
	var m=3D document.createElement("div");=0A=
	m.appendChild( document.createTextNode( text ) );=0A=
=0A=
	e.appendChild( m );=0A=
=0A=
	return true;=0A=
}=0A=
=0A=
/**=0A=
* compatibility wrapper for creating a new XMLHttpRequest object.=0A=
*/=0A=
function sajax_init_object() {=0A=
	sajax_debug("sajax_init_object() called..")=0A=
	var A;=0A=
	try {=0A=
		// Try the new style before ActiveX so we don't=0A=
		// unnecessarily trigger warnings in IE 7 when=0A=
		// set to prompt about ActiveX usage=0A=
		A =3D new XMLHttpRequest();=0A=
	} catch (e) {=0A=
		try {=0A=
			A=3Dnew ActiveXObject("Msxml2.XMLHTTP");=0A=
		} catch (e) {=0A=
			try {=0A=
				A=3Dnew ActiveXObject("Microsoft.XMLHTTP");=0A=
			} catch (oc) {=0A=
				A=3Dnull;=0A=
			}=0A=
		}=0A=
	}=0A=
	if (!A)=0A=
		sajax_debug("Could not create connection object.");=0A=
=0A=
	return A;=0A=
}=0A=
=0A=
/**=0A=
* Perform an ajax call to mediawiki. Calls are handeled by =
AjaxDispatcher.php=0A=
*   func_name - the name of the function to call. Must be registered in =
$wgAjaxExportList=0A=
*   args - an array of arguments to that function=0A=
*   target - the target that will handle the result of the call. If this =
is a function,=0A=
*            if will be called with the XMLHttpRequest as a parameter; =
if it's an input=0A=
*            element, its value will be set to the resultText; if it's =
another type of=0A=
*            element, its innerHTML will be set to the resultText.=0A=
*=0A=
* Example:=0A=
*    sajax_do_call('doFoo', [1, 2, 3], =
document.getElementById("showFoo"));=0A=
*=0A=
* This will call the doFoo function via MediaWiki's AjaxDispatcher, with=0A=
* (1, 2, 3) as the parameter list, and will show the result in the =
element=0A=
* with id =3D showFoo=0A=
*/=0A=
function sajax_do_call(func_name, args, target) {=0A=
	var i, x, n;=0A=
	var uri;=0A=
	var post_data;=0A=
	uri =3D wgServer +=0A=
		((wgScript =3D=3D null) ? (wgScriptPath + "/index.php") : wgScript) +=0A=
		"?action=3Dajax";=0A=
	if (sajax_request_type =3D=3D "GET") {=0A=
		if (uri.indexOf("?") =3D=3D -1)=0A=
			uri =3D uri + "?rs=3D" + encodeURIComponent(func_name);=0A=
		else=0A=
			uri =3D uri + "&rs=3D" + encodeURIComponent(func_name);=0A=
		for (i =3D 0; i < args.length; i++)=0A=
			uri =3D uri + "&rsargs[]=3D" + encodeURIComponent(args[i]);=0A=
		//uri =3D uri + "&rsrnd=3D" + new Date().getTime();=0A=
		post_data =3D null;=0A=
	} else {=0A=
		post_data =3D "rs=3D" + encodeURIComponent(func_name);=0A=
		for (i =3D 0; i < args.length; i++)=0A=
			post_data =3D post_data + "&rsargs[]=3D" + =
encodeURIComponent(args[i]);=0A=
	}=0A=
	x =3D sajax_init_object();=0A=
	if (!x) {=0A=
		alert("AJAX not supported");=0A=
		return false;=0A=
	}=0A=
=0A=
	try {=0A=
		x.open(sajax_request_type, uri, true);=0A=
	} catch (e) {=0A=
		if (window.location.hostname =3D=3D "localhost") {=0A=
			alert("Your browser blocks XMLHttpRequest to 'localhost', try using a =
real hostname for development/testing.");=0A=
		}=0A=
		throw e;=0A=
	}=0A=
	if (sajax_request_type =3D=3D "POST") {=0A=
		x.setRequestHeader("Method", "POST " + uri + " HTTP/1.1");=0A=
		x.setRequestHeader("Content-Type", =
"application/x-www-form-urlencoded");=0A=
	}=0A=
	x.setRequestHeader("Pragma", "cache=3Dyes");=0A=
	x.setRequestHeader("Cache-Control", "no-transform");=0A=
	x.onreadystatechange =3D function() {=0A=
		if (x.readyState !=3D 4)=0A=
			return;=0A=
=0A=
		sajax_debug("received (" + x.status + " " + x.statusText + ") " + =
x.responseText);=0A=
=0A=
		//if (x.status !=3D 200)=0A=
		//	alert("Error: " + x.status + " " + x.statusText + ": " + =
x.responseText);=0A=
		//else=0A=
=0A=
		if ( typeof( target ) =3D=3D 'function' ) {=0A=
			target( x );=0A=
		}=0A=
		else if ( typeof( target ) =3D=3D 'object' ) {=0A=
			if ( target.tagName =3D=3D 'INPUT' ) {=0A=
				if (x.status =3D=3D 200) target.value=3D x.responseText;=0A=
				//else alert("Error: " + x.status + " " + x.statusText + " (" + =
x.responseText + ")");=0A=
			}=0A=
			else {=0A=
				if (x.status =3D=3D 200) target.innerHTML =3D x.responseText;=0A=
				else target.innerHTML=3D "<div class=3D'error'>Error: " + x.status + =
" " + x.statusText + " (" + x.responseText + ")</div>";=0A=
			}=0A=
		}=0A=
		else {=0A=
			alert("bad target for sajax_do_call: not a function or object: " + =
target);=0A=
		}=0A=
=0A=
		return;=0A=
	}=0A=
=0A=
	sajax_debug(func_name + " uri =3D " + uri + " / post =3D " + post_data);=0A=
	x.send(post_data);=0A=
	sajax_debug(func_name + " waiting..");=0A=
	delete x;=0A=
=0A=
	return true;=0A=
}=0A=
=0A=
/**=0A=
 * @return boolean whether the browser supports XMLHttpRequest=0A=
 */=0A=
function wfSupportsAjax() {=0A=
	var request =3D sajax_init_object();=0A=
	var supportsAjax =3D request ? true : false;=0A=
	delete request;=0A=
	return supportsAjax;=0A=
}=0A=
=0A=

------=_NextPart_000_0049_01CA353D.AD380F90
Content-Type: application/octet-stream
Content-Transfer-Encoding: quoted-printable
Content-Location: http://en.wikipedia.org/skins-1.5/common/mwsuggest.js?233zz2

/*=0A=
 * OpenSearch ajax suggestion engine for MediaWiki=0A=
 *=0A=
 * uses core MediaWiki open search support to fetch suggestions=0A=
 * and show them below search boxes and other inputs=0A=
 *=0A=
 * by Robert Stojnic (April 2008)=0A=
 */=0A=
=0A=
// search_box_id -> Results object=0A=
var os_map =3D {};=0A=
// cached data, url -> json_text=0A=
var os_cache =3D {};=0A=
// global variables for suggest_keypress=0A=
var os_cur_keypressed =3D 0;=0A=
var os_last_keypress =3D 0;=0A=
var os_keypressed_count =3D 0;=0A=
// type: Timer=0A=
var os_timer =3D null;=0A=
// tie mousedown/up events=0A=
var os_mouse_pressed =3D false;=0A=
var os_mouse_num =3D -1;=0A=
// if true, the last change was made by mouse (and not keyboard)=0A=
var os_mouse_moved =3D false;=0A=
// delay between keypress and suggestion (in ms)=0A=
var os_search_timeout =3D 250;=0A=
// these pairs of inputs/forms will be autoloaded at startup=0A=
var os_autoload_inputs =3D new Array('searchInput', 'searchInput2', =
'powerSearchText', 'searchText');=0A=
var os_autoload_forms =3D new Array('searchform', 'searchform2', =
'powersearch', 'search' );=0A=
// if we stopped the service=0A=
var os_is_stopped =3D false;=0A=
// max lines to show in suggest table=0A=
var os_max_lines_per_suggest =3D 7;=0A=
// number of steps to animate expansion/contraction of container width=0A=
var os_animation_steps =3D 6;=0A=
// num of pixels of smallest step=0A=
var os_animation_min_step =3D 2;=0A=
// delay between steps (in ms)=0A=
var os_animation_delay =3D 30;=0A=
// max width of container in percent of normal size (1 =3D=3D 100%)=0A=
var os_container_max_width =3D 2;=0A=
// currently active animation timer=0A=
var os_animation_timer =3D null;=0A=
=0A=
/** Timeout timer class that will fetch the results */=0A=
function os_Timer(id,r,query){=0A=
	this.id =3D id;=0A=
	this.r =3D r;=0A=
	this.query =3D query;=0A=
}=0A=
=0A=
/** Timer user to animate expansion/contraction of container width */=0A=
function os_AnimationTimer(r, target){=0A=
	this.r =3D r;=0A=
	var current =3D document.getElementById(r.container).offsetWidth;=0A=
	this.inc =3D Math.round((target-current) / os_animation_steps);=0A=
	if(this.inc < os_animation_min_step && this.inc >=3D0)=0A=
		this.inc =3D os_animation_min_step; // minimal animation step=0A=
	if(this.inc > -os_animation_min_step && this.inc <0)=0A=
		this.inc =3D -os_animation_min_step;=0A=
	this.target =3D target;=0A=
}=0A=
=0A=
/** Property class for single search box */=0A=
function os_Results(name, formname){=0A=
	this.searchform =3D formname; // id of the searchform=0A=
	this.searchbox =3D name; // id of the searchbox=0A=
	this.container =3D name+"Suggest"; // div that holds results=0A=
	this.resultTable =3D name+"Result"; // id base for the result table =
(+num =3D table row)=0A=
	this.resultText =3D name+"ResultText"; // id base for the spans within =
result tables (+num)=0A=
	this.toggle =3D name+"Toggle"; // div that has the toggle =
(enable/disable) link=0A=
	this.query =3D null; // last processed query=0A=
	this.results =3D null;  // parsed titles=0A=
	this.resultCount =3D 0; // number of results=0A=
	this.original =3D null; // query that user entered=0A=
	this.selected =3D -1; // which result is selected=0A=
	this.containerCount =3D 0; // number of results visible in container=0A=
	this.containerRow =3D 0; // height of result field in the container=0A=
	this.containerTotal =3D 0; // total height of the container will all =
results=0A=
	this.visible =3D false; // if container is visible=0A=
	this.stayHidden =3D false; // don't try to show if lost focus=0A=
}=0A=
=0A=
/** Hide results div */=0A=
function os_hideResults(r){=0A=
	var c =3D document.getElementById(r.container);=0A=
	if(c !=3D null)=0A=
		c.style.visibility =3D "hidden";=0A=
	r.visible =3D false;=0A=
	r.selected =3D -1;=0A=
}=0A=
=0A=
/** Show results div */=0A=
function os_showResults(r){=0A=
	if(os_is_stopped)=0A=
		return;=0A=
	if(r.stayHidden)=0A=
		return=0A=
	os_fitContainer(r);=0A=
	var c =3D document.getElementById(r.container);=0A=
	r.selected =3D -1;=0A=
	if(c !=3D null){=0A=
		c.scrollTop =3D 0;=0A=
		c.style.visibility =3D "visible";=0A=
		r.visible =3D true;=0A=
	}=0A=
}=0A=
=0A=
function os_operaWidthFix(x){=0A=
	// TODO: better css2 incompatibility detection here=0A=
	if(is_opera || is_khtml || =
navigator.userAgent.toLowerCase().indexOf('firefox/1')!=3D-1){=0A=
		return 30; // opera&konqueror & old firefox don't understand =
overflow-x, estimate scrollbar width=0A=
	}=0A=
	return 0;=0A=
}=0A=
=0A=
function os_encodeQuery(value){=0A=
  if (encodeURIComponent) {=0A=
    return encodeURIComponent(value);=0A=
  }=0A=
  if(escape) {=0A=
    return escape(value);=0A=
  }=0A=
  return null;=0A=
}=0A=
function os_decodeValue(value){=0A=
  if (decodeURIComponent) {=0A=
    return decodeURIComponent(value);=0A=
  }=0A=
  if(unescape){=0A=
  	return unescape(value);=0A=
  }=0A=
  return null;=0A=
}=0A=
=0A=
/** Brower-dependent functions to find window inner size, and scroll =
status */=0A=
function f_clientWidth() {=0A=
	return f_filterResults (=0A=
		window.innerWidth ? window.innerWidth : 0,=0A=
		document.documentElement ? document.documentElement.clientWidth : 0,=0A=
		document.body ? document.body.clientWidth : 0=0A=
	);=0A=
}=0A=
function f_clientHeight() {=0A=
	return f_filterResults (=0A=
		window.innerHeight ? window.innerHeight : 0,=0A=
		document.documentElement ? document.documentElement.clientHeight : 0,=0A=
		document.body ? document.body.clientHeight : 0=0A=
	);=0A=
}=0A=
function f_scrollLeft() {=0A=
	return f_filterResults (=0A=
		window.pageXOffset ? window.pageXOffset : 0,=0A=
		document.documentElement ? document.documentElement.scrollLeft : 0,=0A=
		document.body ? document.body.scrollLeft : 0=0A=
	);=0A=
}=0A=
function f_scrollTop() {=0A=
	return f_filterResults (=0A=
		window.pageYOffset ? window.pageYOffset : 0,=0A=
		document.documentElement ? document.documentElement.scrollTop : 0,=0A=
		document.body ? document.body.scrollTop : 0=0A=
	);=0A=
}=0A=
function f_filterResults(n_win, n_docel, n_body) {=0A=
	var n_result =3D n_win ? n_win : 0;=0A=
	if (n_docel && (!n_result || (n_result > n_docel)))=0A=
		n_result =3D n_docel;=0A=
	return n_body && (!n_result || (n_result > n_body)) ? n_body : n_result;=0A=
}=0A=
=0A=
/** Get the height available for the results container */=0A=
function os_availableHeight(r){=0A=
	var absTop =3D document.getElementById(r.container).style.top;=0A=
	var px =3D absTop.lastIndexOf("px");=0A=
	if(px > 0)=0A=
		absTop =3D absTop.substring(0,px);=0A=
	return f_clientHeight() - (absTop - f_scrollTop());=0A=
}=0A=
=0A=
=0A=
/** Get element absolute position {left,top} */=0A=
function os_getElementPosition(elemID){=0A=
	var offsetTrail =3D document.getElementById(elemID);=0A=
	var offsetLeft =3D 0;=0A=
	var offsetTop =3D 0;=0A=
	while (offsetTrail){=0A=
		offsetLeft +=3D offsetTrail.offsetLeft;=0A=
		offsetTop +=3D offsetTrail.offsetTop;=0A=
		offsetTrail =3D offsetTrail.offsetParent;=0A=
	}=0A=
	if (navigator.userAgent.indexOf('Mac') !=3D -1 && typeof =
document.body.leftMargin !=3D 'undefined'){=0A=
		offsetLeft +=3D document.body.leftMargin;=0A=
		offsetTop +=3D document.body.topMargin;=0A=
	}=0A=
	return {left:offsetLeft,top:offsetTop};=0A=
}=0A=
=0A=
/** Create the container div that will hold the suggested titles */=0A=
function os_createContainer(r){=0A=
	var c =3D document.createElement("div");=0A=
	var s =3D document.getElementById(r.searchbox);=0A=
	var pos =3D os_getElementPosition(r.searchbox);=0A=
	var left =3D pos.left;=0A=
	var top =3D pos.top + s.offsetHeight;=0A=
	c.className =3D "os-suggest";=0A=
	c.setAttribute("id", r.container);=0A=
	document.body.appendChild(c);=0A=
=0A=
	// dynamically generated style params=0A=
	// IE workaround, cannot explicitely set "style" attribute=0A=
	c =3D document.getElementById(r.container);=0A=
	c.style.top =3D top+"px";=0A=
	c.style.left =3D left+"px";=0A=
	c.style.width =3D s.offsetWidth+"px";=0A=
=0A=
	// mouse event handlers=0A=
	c.onmouseover =3D function(event) { os_eventMouseover(r.searchbox, =
event); };=0A=
	c.onmousemove =3D function(event) { os_eventMousemove(r.searchbox, =
event); };=0A=
	c.onmousedown =3D function(event) { return =
os_eventMousedown(r.searchbox, event); };=0A=
	c.onmouseup =3D function(event) { os_eventMouseup(r.searchbox, event); =
};=0A=
	return c;=0A=
}=0A=
=0A=
/** change container height to fit to screen */=0A=
function os_fitContainer(r){=0A=
	var c =3D document.getElementById(r.container);=0A=
	var h =3D os_availableHeight(r) - 20;=0A=
	var inc =3D r.containerRow;=0A=
	h =3D parseInt(h/inc) * inc;=0A=
	if(h < (2 * inc) && r.resultCount > 1) // min: two results=0A=
		h =3D 2 * inc;=0A=
	if((h/inc) > os_max_lines_per_suggest )=0A=
		h =3D inc * os_max_lines_per_suggest;=0A=
	if(h < r.containerTotal){=0A=
		c.style.height =3D h +"px";=0A=
		r.containerCount =3D parseInt(Math.round(h/inc));=0A=
	} else{=0A=
		c.style.height =3D r.containerTotal+"px";=0A=
		r.containerCount =3D r.resultCount;=0A=
	}=0A=
}=0A=
/** If some entries are longer than the box, replace text with "..." */=0A=
function os_trimResultText(r){=0A=
	// find max width, first see if we could expand the container to fit it=0A=
	var maxW =3D 0;=0A=
	for(var i=3D0;i<r.resultCount;i++){=0A=
		var e =3D document.getElementById(r.resultText+i);=0A=
		if(e.offsetWidth > maxW)=0A=
			maxW =3D e.offsetWidth;=0A=
	}=0A=
	var w =3D document.getElementById(r.container).offsetWidth;=0A=
	var fix =3D 0;=0A=
	if(r.containerCount < r.resultCount){=0A=
		fix =3D 20; // give 20px for scrollbar=0A=
	} else=0A=
		fix =3D os_operaWidthFix(w);=0A=
	if(fix < 4)=0A=
		fix =3D 4; // basic padding=0A=
	maxW +=3D fix;=0A=
=0A=
	// resize container to fit more data if permitted=0A=
	var normW =3D document.getElementById(r.searchbox).offsetWidth;=0A=
	var prop =3D maxW / normW;=0A=
	if(prop > os_container_max_width)=0A=
		prop =3D os_container_max_width;=0A=
	else if(prop < 1)=0A=
		prop =3D 1;=0A=
	var newW =3D Math.round( normW * prop );=0A=
	if( w !=3D newW ){=0A=
		w =3D newW;=0A=
		if( os_animation_timer !=3D null )=0A=
			clearInterval(os_animation_timer.id)=0A=
		os_animation_timer =3D new os_AnimationTimer(r,w);=0A=
		os_animation_timer.id =3D =
setInterval("os_animateChangeWidth()",os_animation_delay);=0A=
		w -=3D fix; // this much is reserved=0A=
	}=0A=
=0A=
	// trim results=0A=
	if(w < 10)=0A=
		return;=0A=
	for(var i=3D0;i<r.resultCount;i++){=0A=
		var e =3D document.getElementById(r.resultText+i);=0A=
		var replace =3D 1;=0A=
		var lastW =3D e.offsetWidth+1;=0A=
		var iteration =3D 0;=0A=
		var changedText =3D false;=0A=
		while(e.offsetWidth > w && (e.offsetWidth < lastW || iteration<2)){=0A=
			changedText =3D true;=0A=
			lastW =3D e.offsetWidth;=0A=
			var l =3D e.innerHTML;=0A=
			e.innerHTML =3D l.substring(0,l.length-replace)+"...";=0A=
			iteration++;=0A=
			replace =3D 4; // how many chars to replace=0A=
		}=0A=
		if(changedText){=0A=
			// show hint for trimmed titles=0A=
			=
document.getElementById(r.resultTable+i).setAttribute("title",r.results[i=
]);=0A=
		}=0A=
	}=0A=
}=0A=
=0A=
/** Invoked on timer to animate change in container width */=0A=
function os_animateChangeWidth(){=0A=
	var r =3D os_animation_timer.r;=0A=
	var c =3D document.getElementById(r.container);=0A=
	var w =3D c.offsetWidth;=0A=
	var normW =3D document.getElementById(r.searchbox).offsetWidth;=0A=
	var normL =3D os_getElementPosition(r.searchbox).left;=0A=
	var inc =3D os_animation_timer.inc;=0A=
	var target =3D os_animation_timer.target;=0A=
	var nw =3D w + inc;=0A=
	if( (inc > 0 && nw >=3D target) || (inc <=3D 0 && nw <=3D target) ){=0A=
		// finished !=0A=
		c.style.width =3D target+"px";=0A=
		clearInterval(os_animation_timer.id)=0A=
		os_animation_timer =3D null;=0A=
	} else{=0A=
		// in-progress=0A=
		c.style.width =3D nw+"px";=0A=
		if(document.documentElement.dir =3D=3D "rtl")=0A=
			c.style.left =3D (normL + normW + (target - nw) - =
os_animation_timer.target - 1)+"px";=0A=
	}=0A=
}=0A=
=0A=
/** Handles data from XMLHttpRequest, and updates the suggest results */=0A=
function os_updateResults(r, query, text, cacheKey){=0A=
	os_cache[cacheKey] =3D text;=0A=
	r.query =3D query;=0A=
	r.original =3D query;=0A=
	if(text =3D=3D ""){=0A=
		r.results =3D null;=0A=
		r.resultCount =3D 0;=0A=
		os_hideResults(r);=0A=
	} else{=0A=
		try {=0A=
			var p =3D eval('('+text+')'); // simple json parse, could do a safer =
one=0A=
			if(p.length<2 || p[1].length =3D=3D 0){=0A=
				r.results =3D null;=0A=
				r.resultCount =3D 0;=0A=
				os_hideResults(r);=0A=
				return;=0A=
			}=0A=
			var c =3D document.getElementById(r.container);=0A=
			if(c =3D=3D null)=0A=
				c =3D os_createContainer(r);=0A=
			c.innerHTML =3D os_createResultTable(r,p[1]);=0A=
			// init container table sizes=0A=
			var t =3D document.getElementById(r.resultTable);=0A=
			r.containerTotal =3D t.offsetHeight;=0A=
			r.containerRow =3D t.offsetHeight / r.resultCount;=0A=
			os_fitContainer(r);=0A=
			os_trimResultText(r);=0A=
			os_showResults(r);=0A=
		} catch(e){=0A=
			// bad response from server or such=0A=
			os_hideResults(r);=0A=
			os_cache[cacheKey] =3D null;=0A=
		}=0A=
	}=0A=
}=0A=
=0A=
/** Create the result table to be placed in the container div */=0A=
function os_createResultTable(r, results){=0A=
	var c =3D document.getElementById(r.container);=0A=
	var width =3D c.offsetWidth - os_operaWidthFix(c.offsetWidth);=0A=
	var html =3D "<table class=3D\"os-suggest-results\" =
id=3D\""+r.resultTable+"\" style=3D\"width: "+width+"px;\">";=0A=
	r.results =3D new Array();=0A=
	r.resultCount =3D results.length;=0A=
	for(i=3D0;i<results.length;i++){=0A=
		var title =3D os_decodeValue(results[i]);=0A=
		r.results[i] =3D title;=0A=
		html +=3D "<tr><td class=3D\"os-suggest-result\" =
id=3D\""+r.resultTable+i+"\"><span =
id=3D\""+r.resultText+i+"\">"+title+"</span></td></tr>";=0A=
	}=0A=
	html+=3D"</table>"=0A=
	return html;=0A=
}=0A=
=0A=
/** Fetch namespaces from checkboxes or hidden fields in the search form,=0A=
    if none defined use wgSearchNamespaces global */=0A=
function os_getNamespaces(r){=0A=
	var namespaces =3D "";=0A=
	var elements =3D document.forms[r.searchform].elements;=0A=
	for(i=3D0; i < elements.length; i++){=0A=
		var name =3D elements[i].name;=0A=
		if(typeof name !=3D 'undefined' && name.length > 2=0A=
		&& name[0]=3D=3D'n' && name[1]=3D=3D's'=0A=
		&& ((elements[i].type=3D=3D'checkbox' && elements[i].checked)=0A=
		 	|| (elements[i].type=3D=3D'hidden' && elements[i].value=3D=3D"1")) ){=0A=
			if(namespaces!=3D"")=0A=
				namespaces+=3D"|";=0A=
			namespaces+=3Dname.substring(2);=0A=
		}=0A=
	}=0A=
	if(namespaces =3D=3D "")=0A=
		namespaces =3D wgSearchNamespaces.join("|");=0A=
	return namespaces;=0A=
}=0A=
=0A=
/** Update results if user hasn't already typed something else */=0A=
function os_updateIfRelevant(r, query, text, cacheKey){=0A=
	var t =3D document.getElementById(r.searchbox);=0A=
	if(t !=3D null && t.value =3D=3D query){ // check if response is still =
relevant=0A=
		os_updateResults(r, query, text, cacheKey);=0A=
	}=0A=
	r.query =3D query;=0A=
}=0A=
=0A=
/** Fetch results after some timeout */=0A=
function os_delayedFetch(){=0A=
	if(os_timer =3D=3D null)=0A=
		return;=0A=
	var r =3D os_timer.r;=0A=
	var query =3D os_timer.query;=0A=
	os_timer =3D null;=0A=
	var path =3D =
wgMWSuggestTemplate.replace("{namespaces}",os_getNamespaces(r))=0A=
							  	  .replace("{dbname}",wgDBname)=0A=
							  	  .replace("{searchTerms}",os_encodeQuery(query));=0A=
=0A=
	// try to get from cache, if not fetch using ajax=0A=
	var cached =3D os_cache[path];=0A=
	if(cached !=3D null){=0A=
		os_updateIfRelevant(r, query, cached, path);=0A=
	} else{=0A=
		var xmlhttp =3D sajax_init_object();=0A=
		if(xmlhttp){=0A=
			try {=0A=
				xmlhttp.open("GET", path, true);=0A=
				xmlhttp.onreadystatechange=3Dfunction(){=0A=
		        	if (xmlhttp.readyState=3D=3D4 && typeof os_updateIfRelevant =
=3D=3D 'function') {=0A=
		        		os_updateIfRelevant(r, query, xmlhttp.responseText, path);=0A=
	        		}=0A=
	      		};=0A=
	     		xmlhttp.send(null);=0A=
	     	} catch (e) {=0A=
				if (window.location.hostname =3D=3D "localhost") {=0A=
					alert("Your browser blocks XMLHttpRequest to 'localhost', try using =
a real hostname for development/testing.");=0A=
				}=0A=
				throw e;=0A=
			}=0A=
		}=0A=
	}=0A=
}=0A=
=0A=
/** Init timed update via os_delayedUpdate() */=0A=
function os_fetchResults(r, query, timeout){=0A=
	if(query =3D=3D ""){=0A=
		r.query =3D "";=0A=
		os_hideResults(r);=0A=
		return;=0A=
	} else if(query =3D=3D r.query)=0A=
		return; // no change=0A=
=0A=
	os_is_stopped =3D false; // make sure we're running=0A=
=0A=
	/* var cacheKey =3D wgDBname+":"+query;=0A=
	var cached =3D os_cache[cacheKey];=0A=
	if(cached !=3D null){=0A=
		os_updateResults(r,wgDBname,query,cached);=0A=
		return;=0A=
	} */=0A=
=0A=
	// cancel any pending fetches=0A=
	if(os_timer !=3D null && os_timer.id !=3D null)=0A=
		clearTimeout(os_timer.id);=0A=
	// schedule delayed fetching of results=0A=
	if(timeout !=3D 0){=0A=
		os_timer =3D new =
os_Timer(setTimeout("os_delayedFetch()",timeout),r,query);=0A=
	} else{=0A=
		os_timer =3D new os_Timer(null,r,query);=0A=
		os_delayedFetch(); // do it now!=0A=
	}=0A=
=0A=
}=0A=
/** Change the highlighted row (i.e. suggestion), from position cur to =
next */=0A=
function os_changeHighlight(r, cur, next, updateSearchBox){=0A=
	if (next >=3D r.resultCount)=0A=
		next =3D r.resultCount-1;=0A=
	if (next < -1)=0A=
		next =3D -1;=0A=
	r.selected =3D next;=0A=
   	if (cur =3D=3D next)=0A=
    	return; // nothing to do.=0A=
=0A=
    if(cur >=3D 0){=0A=
    	var curRow =3D document.getElementById(r.resultTable + cur);=0A=
    	if(curRow !=3D null)=0A=
    		curRow.className =3D "os-suggest-result";=0A=
    }=0A=
    var newText;=0A=
    if(next >=3D 0){=0A=
    	var nextRow =3D document.getElementById(r.resultTable + next);=0A=
    	if(nextRow !=3D null)=0A=
    		nextRow.className =3D os_HighlightClass();=0A=
    	newText =3D r.results[next];=0A=
    } else=0A=
    	newText =3D r.original;=0A=
=0A=
    // adjust the scrollbar if any=0A=
    if(r.containerCount < r.resultCount){=0A=
    	var c =3D document.getElementById(r.container);=0A=
    	var vStart =3D c.scrollTop / r.containerRow;=0A=
    	var vEnd =3D vStart + r.containerCount;=0A=
    	if(next < vStart)=0A=
    		c.scrollTop =3D next * r.containerRow;=0A=
    	else if(next >=3D vEnd)=0A=
    		c.scrollTop =3D (next - r.containerCount + 1) * r.containerRow;=0A=
    }=0A=
=0A=
    // update the contents of the search box=0A=
    if(updateSearchBox){=0A=
    	os_updateSearchQuery(r,newText);=0A=
    }=0A=
}=0A=
=0A=
function os_HighlightClass() {=0A=
	var match =3D navigator.userAgent.match(/AppleWebKit\/(\d+)/);=0A=
	if (match) {=0A=
		var webKitVersion =3D parseInt(match[1]);=0A=
		if (webKitVersion < 523) {=0A=
			// CSS system highlight colors broken on old Safari=0A=
			// https://bugs.webkit.org/show_bug.cgi?id=3D6129=0A=
			// Safari 3.0.4, 3.1 known ok=0A=
			return "os-suggest-result-hl-webkit";=0A=
		}=0A=
	}=0A=
	return "os-suggest-result-hl";=0A=
}=0A=
=0A=
function os_updateSearchQuery(r,newText){=0A=
	document.getElementById(r.searchbox).value =3D newText;=0A=
    r.query =3D newText;=0A=
}=0A=
=0A=
/** Find event target */=0A=
function os_getTarget(e){=0A=
	if (!e) e =3D window.event;=0A=
	if (e.target) return e.target;=0A=
	else if (e.srcElement) return e.srcElement;=0A=
	else return null;=0A=
}=0A=
=0A=
=0A=
=0A=
/********************=0A=
 *  Keyboard events=0A=
 ********************/=0A=
=0A=
/** Event handler that will fetch results on keyup */=0A=
function os_eventKeyup(e){=0A=
	var targ =3D os_getTarget(e);=0A=
	var r =3D os_map[targ.id];=0A=
	if(r =3D=3D null)=0A=
		return; // not our event=0A=
=0A=
	// some browsers won't generate keypressed for arrow keys, catch it=0A=
	if(os_keypressed_count =3D=3D 0){=0A=
		os_processKey(r,os_cur_keypressed,targ);=0A=
	}=0A=
	var query =3D targ.value;=0A=
	os_fetchResults(r,query,os_search_timeout);=0A=
}=0A=
=0A=
/** catch arrows up/down and escape to hide the suggestions */=0A=
function os_processKey(r,keypressed,targ){=0A=
	if (keypressed =3D=3D 40){ // Arrow Down=0A=
    	if (r.visible) {=0A=
      		os_changeHighlight(r, r.selected, r.selected+1, true);=0A=
    	} else if(os_timer =3D=3D null){=0A=
    		// user wants to get suggestions now=0A=
    		r.query =3D "";=0A=
			os_fetchResults(r,targ.value,0);=0A=
    	}=0A=
  	} else if (keypressed =3D=3D 38){ // Arrow Up=0A=
  		if (r.visible){=0A=
  			os_changeHighlight(r, r.selected, r.selected-1, true);=0A=
  		}=0A=
  	} else if(keypressed =3D=3D 27){ // Escape=0A=
  		document.getElementById(r.searchbox).value =3D r.original;=0A=
  		r.query =3D r.original;=0A=
  		os_hideResults(r);=0A=
  	} else if(r.query !=3D document.getElementById(r.searchbox).value){=0A=
  		// os_hideResults(r); // don't show old suggestions=0A=
  	}=0A=
}=0A=
=0A=
/** When keys is held down use a timer to output regular events */=0A=
function os_eventKeypress(e){=0A=
	var targ =3D os_getTarget(e);=0A=
	var r =3D os_map[targ.id];=0A=
	if(r =3D=3D null)=0A=
		return; // not our event=0A=
=0A=
	var keypressed =3D os_cur_keypressed;=0A=
	if(keypressed =3D=3D 38 || keypressed =3D=3D 40){=0A=
		var d =3D new Date()=0A=
		var now =3D d.getTime();=0A=
		if(now - os_last_keypress < 120){=0A=
			os_last_keypress =3D now;=0A=
			return;=0A=
		}=0A=
	}=0A=
=0A=
	os_keypressed_count++;=0A=
	os_processKey(r,keypressed,targ);=0A=
}=0A=
=0A=
/** Catch the key code (Firefox bug)  */=0A=
function os_eventKeydown(e){=0A=
	if (!e) e =3D window.event;=0A=
	var targ =3D os_getTarget(e);=0A=
	var r =3D os_map[targ.id];=0A=
	if(r =3D=3D null)=0A=
		return; // not our event=0A=
=0A=
	os_mouse_moved =3D false;=0A=
=0A=
	os_cur_keypressed =3D (e.keyCode =3D=3D undefined) ? e.which : =
e.keyCode;=0A=
	os_last_keypress =3D 0;=0A=
	os_keypressed_count =3D 0;=0A=
}=0A=
=0A=
/** Event: loss of focus of input box */=0A=
function os_eventBlur(e){=0A=
	var targ =3D os_getTarget(e);=0A=
	var r =3D os_map[targ.id];=0A=
	if(r =3D=3D null)=0A=
		return; // not our event=0A=
	if(!os_mouse_pressed){=0A=
		os_hideResults(r);=0A=
		// force canvas to stay hidden=0A=
		r.stayHidden =3D true=0A=
		// cancel any pending fetches=0A=
		if(os_timer !=3D null && os_timer.id !=3D null)=0A=
			clearTimeout(os_timer.id);=0A=
		os_timer =3D null=0A=
	}=0A=
}=0A=
=0A=
/** Event: focus (catch only when stopped) */=0A=
function os_eventFocus(e){=0A=
	var targ =3D os_getTarget(e);=0A=
	var r =3D os_map[targ.id];=0A=
	if(r =3D=3D null)=0A=
		return; // not our event=0A=
	r.stayHidden =3D false=0A=
}=0A=
=0A=
=0A=
=0A=
/********************=0A=
 *  Mouse events=0A=
 ********************/=0A=
=0A=
/** Mouse over the container */=0A=
function os_eventMouseover(srcId, e){=0A=
	var targ =3D os_getTarget(e);=0A=
	var r =3D os_map[srcId];=0A=
	if(r =3D=3D null || !os_mouse_moved)=0A=
		return; // not our event=0A=
	var num =3D os_getNumberSuffix(targ.id);=0A=
	if(num >=3D 0)=0A=
		os_changeHighlight(r,r.selected,num,false);=0A=
=0A=
}=0A=
=0A=
/* Get row where the event occured (from its id) */=0A=
function os_getNumberSuffix(id){=0A=
	var num =3D id.substring(id.length-2);=0A=
	if( ! (num.charAt(0) >=3D '0' && num.charAt(0) <=3D '9') )=0A=
		num =3D num.substring(1);=0A=
	if(os_isNumber(num))=0A=
		return parseInt(num);=0A=
	else=0A=
		return -1;=0A=
}=0A=
=0A=
/** Save mouse move as last action */=0A=
function os_eventMousemove(srcId, e){=0A=
	os_mouse_moved =3D true;=0A=
}=0A=
=0A=
/** Mouse button held down, register possible click  */=0A=
function os_eventMousedown(srcId, e){=0A=
	var targ =3D os_getTarget(e);=0A=
	var r =3D os_map[srcId];=0A=
	if(r =3D=3D null)=0A=
		return; // not our event=0A=
	var num =3D os_getNumberSuffix(targ.id);=0A=
=0A=
	os_mouse_pressed =3D true;=0A=
	if(num >=3D 0){=0A=
		os_mouse_num =3D num;=0A=
		// os_updateSearchQuery(r,r.results[num]);=0A=
	}=0A=
	// keep the focus on the search field=0A=
	document.getElementById(r.searchbox).focus();=0A=
=0A=
	return false; // prevents selection=0A=
}=0A=
=0A=
/** Mouse button released, check for click on some row */=0A=
function os_eventMouseup(srcId, e){=0A=
	var targ =3D os_getTarget(e);=0A=
	var r =3D os_map[srcId];=0A=
	if(r =3D=3D null)=0A=
		return; // not our event=0A=
	var num =3D os_getNumberSuffix(targ.id);=0A=
=0A=
	if(num >=3D 0 && os_mouse_num =3D=3D num){=0A=
		os_updateSearchQuery(r,r.results[num]);=0A=
		os_hideResults(r);=0A=
		document.getElementById(r.searchform).submit();=0A=
	}=0A=
	os_mouse_pressed =3D false;=0A=
	// keep the focus on the search field=0A=
	document.getElementById(r.searchbox).focus();=0A=
}=0A=
=0A=
/** Check if x is a valid integer */=0A=
function os_isNumber(x){=0A=
	if(x =3D=3D "" || isNaN(x))=0A=
		return false;=0A=
	for(var i=3D0;i<x.length;i++){=0A=
		var c =3D x.charAt(i);=0A=
		if( ! (c >=3D '0' && c <=3D '9') )=0A=
			return false;=0A=
	}=0A=
	return true;=0A=
}=0A=
=0A=
=0A=
/** When the form is submitted hide everything, cancel updates... */=0A=
function os_eventOnsubmit(e){=0A=
	var targ =3D os_getTarget(e);=0A=
=0A=
	os_is_stopped =3D true;=0A=
	// kill timed requests=0A=
	if(os_timer !=3D null && os_timer.id !=3D null){=0A=
		clearTimeout(os_timer.id);=0A=
		os_timer =3D null;=0A=
	}=0A=
	// Hide all suggestions=0A=
	for(i=3D0;i<os_autoload_inputs.length;i++){=0A=
		var r =3D os_map[os_autoload_inputs[i]];=0A=
		if(r !=3D null){=0A=
			var b =3D document.getElementById(r.searchform);=0A=
			if(b !=3D null && b =3D=3D targ){=0A=
				// set query value so the handler won't try to fetch additional =
results=0A=
				r.query =3D document.getElementById(r.searchbox).value;=0A=
			}=0A=
			os_hideResults(r);=0A=
		}=0A=
	}=0A=
	return true;=0A=
}=0A=
=0A=
function os_hookEvent(element, hookName, hookFunct) {=0A=
	if (element.addEventListener) {=0A=
		element.addEventListener(hookName, hookFunct, false);=0A=
	} else if (window.attachEvent) {=0A=
		element.attachEvent("on" + hookName, hookFunct);=0A=
	}=0A=
}=0A=
=0A=
/** Init Result objects and event handlers */=0A=
function os_initHandlers(name, formname, element){=0A=
	var r =3D new os_Results(name, formname);=0A=
	// event handler=0A=
	os_hookEvent(element, "keyup", function(event) { os_eventKeyup(event); =
});=0A=
	os_hookEvent(element, "keydown", function(event) { =
os_eventKeydown(event); });=0A=
	os_hookEvent(element, "keypress", function(event) { =
os_eventKeypress(event); });=0A=
	os_hookEvent(element, "blur", function(event) { os_eventBlur(event); });=0A=
	os_hookEvent(element, "focus", function(event) { os_eventFocus(event); =
});=0A=
	element.setAttribute("autocomplete","off");=0A=
	// stopping handler=0A=
	os_hookEvent(document.getElementById(formname), "submit", =
function(event){ return os_eventOnsubmit(event); });=0A=
	os_map[name] =3D r;=0A=
	// toggle link=0A=
	if(document.getElementById(r.toggle) =3D=3D null){=0A=
		// TODO: disable this while we figure out a way for this to work in =
all browsers=0A=
		/* if(name=3D=3D'searchInput'){=0A=
			// special case: place above the main search box=0A=
			var t =3D os_createToggle(r,"os-suggest-toggle");=0A=
			var searchBody =3D document.getElementById('searchBody');=0A=
			var first =3D =
searchBody.parentNode.firstChild.nextSibling.appendChild(t);=0A=
		} else{=0A=
			// default: place below search box to the right=0A=
			var t =3D os_createToggle(r,"os-suggest-toggle-def");=0A=
			var top =3D element.offsetTop + element.offsetHeight;=0A=
			var left =3D element.offsetLeft + element.offsetWidth;=0A=
			t.style.position =3D "absolute";=0A=
			t.style.top =3D top + "px";=0A=
			t.style.left =3D left + "px";=0A=
			element.parentNode.appendChild(t);=0A=
			// only now width gets calculated, shift right=0A=
			left -=3D t.offsetWidth;=0A=
			t.style.left =3D left + "px";=0A=
			t.style.visibility =3D "visible";=0A=
		} */=0A=
	}=0A=
=0A=
}=0A=
=0A=
/** Return the span element that contains the toggle link */=0A=
function os_createToggle(r,className){=0A=
	var t =3D document.createElement("span");=0A=
	t.className =3D className;=0A=
	t.setAttribute("id", r.toggle);=0A=
	var link =3D document.createElement("a");=0A=
	link.setAttribute("href","javascript:void(0);");=0A=
	link.onclick =3D function(){ os_toggle(r.searchbox,r.searchform) };=0A=
	var msg =3D document.createTextNode(wgMWSuggestMessages[0]);=0A=
	link.appendChild(msg);=0A=
	t.appendChild(link);=0A=
	return t;=0A=
}=0A=
=0A=
/** Call when user clicks on some of the toggle links */=0A=
function os_toggle(inputId,formName){=0A=
	r =3D os_map[inputId];=0A=
	var msg =3D '';=0A=
	if(r =3D=3D null){=0A=
		os_enableSuggestionsOn(inputId,formName);=0A=
		r =3D os_map[inputId];=0A=
		msg =3D wgMWSuggestMessages[0];=0A=
	} else{=0A=
		os_disableSuggestionsOn(inputId,formName);=0A=
		msg =3D wgMWSuggestMessages[1];=0A=
	}=0A=
	// change message=0A=
	var link =3D document.getElementById(r.toggle).firstChild;=0A=
	link.replaceChild(document.createTextNode(msg),link.firstChild);=0A=
}=0A=
=0A=
/** Call this to enable suggestions on input (id=3DinputId), on a form =
(name=3DformName) */=0A=
function os_enableSuggestionsOn(inputId, formName){=0A=
	os_initHandlers( inputId, formName, document.getElementById(inputId) );=0A=
}=0A=
=0A=
/** Call this to disable suggestios on input box (id=3DinputId) */=0A=
function os_disableSuggestionsOn(inputId){=0A=
	r =3D os_map[inputId];=0A=
	if(r !=3D null){=0A=
		// cancel/hide results=0A=
		os_timer =3D null;=0A=
		os_hideResults(r);=0A=
		// turn autocomplete on !=0A=
		document.getElementById(inputId).setAttribute("autocomplete","on");=0A=
		// remove descriptor=0A=
		os_map[inputId] =3D null;=0A=
	}=0A=
}=0A=
=0A=
/** Initialization, call upon page onload */=0A=
function os_MWSuggestInit() {=0A=
	for(i=3D0;i<os_autoload_inputs.length;i++){=0A=
		var id =3D os_autoload_inputs[i];=0A=
		var form =3D os_autoload_forms[i];=0A=
		element =3D document.getElementById( id );=0A=
		if(element !=3D null)=0A=
			os_initHandlers(id,form,element);=0A=
	}=0A=
}=0A=
=0A=
hookEvent("load", os_MWSuggestInit);=0A=
=0A=

------=_NextPart_000_0049_01CA353D.AD380F90
Content-Type: application/octet-stream
Content-Transfer-Encoding: quoted-printable
Content-Location: http://upload.wikimedia.org/centralnotice/wikipedia/en/centralnotice.js?233zz2

=0A=
function toggleNotice() {=0A=
	var notice =3D document.getElementById('centralNotice');=0A=
	if (!wgNoticeToggleState) {=0A=
		notice.className =3D notice.className.replace('collapsed', 'expanded');=0A=
		toggleNoticeCookie('0');=0A=
	} else {=0A=
		notice.className =3D notice.className.replace('expanded', 'collapsed');=0A=
		toggleNoticeCookie('1');=0A=
	}=0A=
	wgNoticeToggleState =3D !wgNoticeToggleState;=0A=
}=0A=
function toggleNoticeStyle(elems, display) {=0A=
	if(elems)=0A=
		for(var i=3D0;i<elems.length;i++)=0A=
			elems[i].style.display =3D display;=0A=
}=0A=
function toggleNoticeCookie(state) {=0A=
	var e =3D new Date();=0A=
	e.setTime( e.getTime() + (7*24*60*60*1000) ); // one week=0A=
	var work=3D'hidesnmessage=3D'+state+'; expires=3D' + e.toGMTString() + =
'; path=3D/';=0A=
	document.cookie =3D work;=0A=
}=0A=
function pickTemplate(templates, weights) {=0A=
	var weightedTemplates =3D new Array();=0A=
	var currentTemplate =3D 0;=0A=
	var totalWeight =3D 0;=0A=
=0A=
	if (templates.length =3D=3D 0)=0A=
		return '';=0A=
=0A=
	while (currentTemplate < templates.length) {=0A=
		totalWeight +=3D weights[currentTemplate];=0A=
		for (i=3D0; i<weights[currentTemplate]; i++) {=0A=
			weightedTemplates[weightedTemplates.length] =3D =
templates[currentTemplate];=0A=
		}=0A=
		currentTemplate++;=0A=
	}=0A=
	=0A=
	if (totalWeight =3D=3D 0)=0A=
		return '';=0A=
=0A=
	var randomnumber=3DMath.floor(Math.random()*totalWeight);=0A=
	return weightedTemplates[randomnumber];=0A=
}=0A=
=0A=
=0A=
var wgNoticeToggleState =3D =
(document.cookie.indexOf('hidesnmessage=3D1')=3D=3D-1);=0A=
document.writeln("\x3cstyle type=3D\"text/css\"\x3e\n#centralNotice =
.siteNoticeSmall{display:none;}\n#centralNotice =
.siteNoticeSmallAnon{display:none;}\n#centralNotice =
.siteNoticeSmallUser{display:none;}\n#centralNotice.collapsed =
.siteNoticeBig{display:none;}\n#centralNotice.collapsed =
.siteNoticeSmall{display:block;}\n#centralNotice.collapsed =
.siteNoticeSmallUser{display:block;}\n#centralNotice.collapsed =
.siteNoticeSmallAnon{display:block;}\n#centralNotice.anonnotice =
.siteNoticeSmallUser{display:none =
!important;}\n#centralNotice.usernotice =
.siteNoticeSmallAnon{display:none !important;}\n\x3c/style\x3e");=0A=
=0A=
wgNotice=3DpickTemplate([],[]);=0A=
if (wgNotice !=3D '')=0A=
wgNotice=3D'<div id=3D"centralNotice" class=3D"' + (wgNoticeToggleState =
? 'expanded' : 'collapsed') + ' ' + (wgUserName ? 'usernotice' : =
'anonnotice' ) + '">' + wgNotice+'</div>';=0A=

------=_NextPart_000_0049_01CA353D.AD380F90
Content-Type: application/octet-stream
Content-Transfer-Encoding: quoted-printable
Content-Location: http://en.wikipedia.org/w/index.php?title=-&action=raw&gen=js&useskin=monobook

/* generated javascript */=0A=
var skin =3D 'monobook';=0A=
var stylepath =3D '/skins-1.5';=0A=
=0A=
/* MediaWiki:Common.js */=0A=
//<source lang=3D"javascript">=0A=
=0A=
/* Import more specific scripts if necessary */=0A=
=0A=
if (wgAction =3D=3D "edit" || wgAction =3D=3D "submit" || wgPageName =
=3D=3D "Special:Upload") //scripts specific to editing pages=0A=
{=0A=
    importScript("MediaWiki:Common.js/edit.js")=0A=
}=0A=
else if (wgPageName =3D=3D "Special:Watchlist") //watchlist scripts=0A=
{=0A=
    importScript("MediaWiki:Common.js/watchlist.js")=0A=
}=0A=
=0A=
=0A=
/** Sysop Javascript =
*******************************************************=0A=
  *=0A=
  *  Description: Allows for sysop-specific Javascript at =
[[MediaWiki:Sysop.js]].=0A=
  */=0A=
function sysopFunctions() {=0A=
    if ( wgUserGroups && !window.disableSysopJS ) {=0A=
        for ( var g =3D 0; g < wgUserGroups.length; ++g ) {=0A=
            if ( wgUserGroups[g] =3D=3D "sysop" ) {=0A=
                importScript( "MediaWiki:Sysop.js" );=0A=
                break;=0A=
            }=0A=
        }=0A=
    }=0A=
}=0A=
=0A=
addOnloadHook( sysopFunctions );=0A=
=0A=
=0A=
/** WikiMiniAtlas *******************************************************=0A=
  *=0A=
  *  Description: WikiMiniAtlas is a popup click and drag world map.=0A=
  *               This script causes all of our coordinate links to =
display the WikiMiniAtlas popup button.=0A=
  *               The script itself is located on meta because it is =
used by many projects.=0A=
  *               See [[Meta:WikiMiniAtlas]] for more information. =0A=
  *  Maintainers: [[User:Dschwen]]=0A=
  */=0A=
=0A=
if (wgServer =3D=3D "https://secure.wikimedia.org") {=0A=
    var metaBase =3D "https://secure.wikimedia.org/wikipedia/meta";=0A=
} else {=0A=
    var metaBase =3D "http://meta.wikimedia.org";=0A=
}=0A=
importScriptURI(metaBase+"/w/index.php?title=3DMediaWiki:Wikiminiatlas.js=
&action=3Draw&ctype=3Dtext/javascript&smaxage=3D21600&maxage=3D86400")=0A=
=0A=
=0A=
/** Mobile Redirect Helper =
************************************************=0A=
 *=0A=
 *  Redirects to the mobile-optimized gateway at en.m.wikimedia.org=0A=
 *  for viewers on iPhone, iPod Touch, Palm Pre, and Android devices.=0A=
 *=0A=
 *  You can turn off the redirect by setting the cookie =
"stopMobileRedirect=3Dtrue"=0A=
 *=0A=
 *  This code cannot be imported, because the JS only loads after all =
other files=0A=
 *  and this was causing major issues for users with mobile devices. =
Must be loaded=0A=
 *  *before* the images and etc of the page on all mobile devices.=0A=
 *=0A=
 *  Maintainer: [[User:Brion VIBBER]], [[User:hcatlin]]=0A=
 */=0A=
if (/(Android|iPhone|iPod|webOS)/.test(navigator.userAgent)) {=0A=
=0A=
  var wgMainPageName =3D 'Main_Page';=0A=
 =0A=
  var stopMobileRedirectCookieExists =3D function() {=0A=
    return (document.cookie.indexOf("stopMobileRedirect=3Dtrue") >=3D 0);=0A=
  }=0A=
 =0A=
  var mobileSiteLink =3D function() {=0A=
    if (wgCanonicalNamespace =3D=3D 'Special' && =
wgCanonicalSpecialPageName =3D=3D 'Search') {=0A=
        var pageLink =3D '?search=3D' + =
encodeURIComponent(document.getElementById('searchText').value);=0A=
    } else if (wgPageName =3D=3D wgMainPageName) {=0A=
        var pageLink =3D '::Home'; // Special case=0A=
    } else {=0A=
        var pageLink =3D =
encodeURIComponent(wgPageName).replace('%2F','/').replace('%3A',':');=0A=
    }=0A=
    return 'http://' + wgContentLanguage + '.m.wikipedia.org/wiki/' + =
pageLink + "?wasRedirected=3Dtrue"=0A=
  }=0A=
 =0A=
  if (!stopMobileRedirectCookieExists()) {=0A=
    document.location =3D mobileSiteLink();=0A=
  }=0A=
}=0A=
=0A=
=0A=
/* Scripts specific to Internet Explorer */=0A=
=0A=
if (navigator.appName =3D=3D "Microsoft Internet Explorer")=0A=
{=0A=
    /** Internet Explorer bug fix =
**************************************************=0A=
     *=0A=
     *  Description: Fixes IE horizontal scrollbar bug=0A=
     *  Maintainers: [[User:Tom-]]?=0A=
     */=0A=
    =0A=
    var oldWidth;=0A=
    var docEl =3D document.documentElement;=0A=
    =0A=
    function fixIEScroll()=0A=
    {=0A=
        if (!oldWidth || docEl.clientWidth > oldWidth)=0A=
            doFixIEScroll();=0A=
        else=0A=
            setTimeout(doFixIEScroll, 1);=0A=
        =0A=
        oldWidth =3D docEl.clientWidth;=0A=
    }=0A=
    =0A=
    function doFixIEScroll() {=0A=
        docEl.style.overflowX =3D (docEl.scrollWidth - docEl.clientWidth =
< 4) ? "hidden" : "";=0A=
    }=0A=
    =0A=
    document.attachEvent("onreadystatechange", fixIEScroll);=0A=
    document.attachEvent("onresize", fixIEScroll);=0A=
    =0A=
    =0A=
    /**=0A=
     * Remove need for CSS hacks regarding MSIE and IPA.=0A=
     */=0A=
    if (document.createStyleSheet) {=0A=
        document.createStyleSheet().addRule('.IPA', 'font-family: =
"Doulos SIL", "Charis SIL", Gentium, "DejaVu Sans", Code2000, "TITUS =
Cyberbit Basic", "Arial Unicode MS", "Lucida Sans Unicode", "Chrysanthi =
Unicode";');=0A=
    }=0A=
=0A=
    // In print IE (7?) does not like line-height=0A=
    appendCSS( '@media print { sup, sub, p, .documentDescription { =
line-height: normal; }}');=0A=
=0A=
    // IE overflow bug=0A=
    appendCSS('div.overflowbugx { overflow-x: scroll !important; =
overflow-y: hidden !important; } div.overflowbugy { overflow-y: scroll =
!important; overflow-x: hidden !important; }');=0A=
    =0A=
    //Import scripts specific to Internet Explorer 6=0A=
    if (navigator.appVersion.substr(22, 1) =3D=3D "6") {=0A=
        importScript("MediaWiki:Common.js/IE60Fixes.js")=0A=
    }=0A=
}=0A=
=0A=
=0A=
/* Test if an element has a certain class =
**************************************=0A=
 *=0A=
 * Description: Uses regular expressions and caching for better =
performance.=0A=
 * Maintainers: [[User:Mike Dillon]], [[User:R. Koot]], [[User:SG]]=0A=
 */=0A=
=0A=
var hasClass =3D (function () {=0A=
    var reCache =3D {};=0A=
    return function (element, className) {=0A=
        return (reCache[className] ? reCache[className] : =
(reCache[className] =3D new RegExp("(?:\\s|^)" + className + =
"(?:\\s|$)"))).test(element.className);=0A=
    };=0A=
})();=0A=
=0A=
=0A=
/** Interwiki links to featured articles =
***************************************=0A=
 *=0A=
 *  Description: Highlights interwiki links to featured articles (or=0A=
 *               equivalents) by changing the bullet before the =
interwiki link=0A=
 *               into a star.=0A=
 *  Maintainers: [[User:R. Koot]]=0A=
 */=0A=
=0A=
function LinkFA() =0A=
{=0A=
    if ( document.getElementById( "p-lang" ) ) {=0A=
        var InterwikiLinks =3D document.getElementById( "p-lang" =
).getElementsByTagName( "li" );=0A=
=0A=
        for ( var i =3D 0; i < InterwikiLinks.length; i++ ) {=0A=
            if ( document.getElementById( InterwikiLinks[i].className + =
"-fa" ) ) {=0A=
                InterwikiLinks[i].className +=3D " FA"=0A=
                InterwikiLinks[i].title =3D "This is a featured article =
in another language.";=0A=
            }=0A=
        }=0A=
    }=0A=
}=0A=
=0A=
addOnloadHook( LinkFA );=0A=
=0A=
=0A=
/** Collapsible tables =
*********************************************************=0A=
 *=0A=
 *  Description: Allows tables to be collapsed, showing only the header. =
See=0A=
 *               [[Wikipedia:NavFrame]].=0A=
 *  Maintainers: [[User:R. Koot]]=0A=
 */=0A=
=0A=
var autoCollapse =3D 2;=0A=
var collapseCaption =3D "hide";=0A=
var expandCaption =3D "show";=0A=
=0A=
function collapseTable( tableIndex )=0A=
{=0A=
    var Button =3D document.getElementById( "collapseButton" + =
tableIndex );=0A=
    var Table =3D document.getElementById( "collapsibleTable" + =
tableIndex );=0A=
=0A=
    if ( !Table || !Button ) {=0A=
        return false;=0A=
    }=0A=
=0A=
    var Rows =3D Table.rows;=0A=
=0A=
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}=0A=
=0A=
function createCollapseButtons()=0A=
{=0A=
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=0A=
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=0A=
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=0A=
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tableIndex );=0A=
=0A=
            var Button     =3D document.createElement( "span" );=0A=
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);=0A=
=0A=
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declared in Common.css=0A=
=0A=
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);=0A=
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+ tableIndex + ");" );=0A=
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=0A=
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=0A=
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=0A=
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}=0A=
=0A=
addOnloadHook( createCollapseButtons );=0A=
=0A=
=0A=
/** Dynamic Navigation Bars (experimental) =
*************************************=0A=
 *=0A=
 *  Description: See [[Wikipedia:NavFrame]].=0A=
 *  Maintainers: UNMAINTAINED=0A=
 */=0A=
=0A=
// set up the words in your language=0A=
var NavigationBarHide =3D '[' + collapseCaption + ']';=0A=
var NavigationBarShow =3D '[' + expandCaption + ']';=0A=
=0A=
// shows and hides content and picture (if available) of navigation bars=0A=
// Parameters:=0A=
//     indexNavigationBar: the index of navigation bar to be toggled=0A=
function toggleNavigationBar(indexNavigationBar)=0A=
{=0A=
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indexNavigationBar);=0A=
=0A=
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=0A=
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NavChild =3D NavChild.nextSibling) {=0A=
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=0A=
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NavChild =3D NavChild.nextSibling) {=0A=
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}=0A=
=0A=
// adds show/hide-button to navigation bars=0A=
function createNavigationBarToggleButton()=0A=
{=0A=
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=0A=
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indexNavigationBar);=0A=
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'javascript:toggleNavigationBar(' + indexNavigationBar + ');');=0A=
=0A=
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             * Check if any children are already hidden.  This loop is =
here for backwards compatibility:=0A=
             * the old way of making NavFrames start out collapsed was =
to manually add style=3D"display:none"=0A=
             * to all the NavPic/NavContent elements.  Since this was =
bad for accessibility (no way to make=0A=
             * the content visible without JavaScript support), the new =
recommended way is to add the class=0A=
             * "collapsed" to the NavFrame itself, just like with =
collapsible tables.=0A=
             */=0A=
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null && !isCollapsed; NavChild =3D NavChild.nextSibling) {=0A=
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NavChild, 'NavContent' ) ) {=0A=
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                        isCollapsed =3D true;=0A=
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null; NavChild =3D NavChild.nextSibling) {=0A=
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NavChild, 'NavContent' ) ) {=0A=
                        NavChild.style.display =3D 'none';=0A=
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                }=0A=
            }=0A=
            var NavToggleText =3D document.createTextNode(isCollapsed ? =
NavigationBarShow : NavigationBarHide);=0A=
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=0A=
            // Find the NavHead and attach the toggle link (Must be this =
complicated because Moz's firstChild handling is borked)=0A=
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}=0A=
=0A=
addOnloadHook( createNavigationBarToggleButton );=0A=
=0A=
=0A=
/** Main Page layout fixes =
*********************************************************=0A=
 *=0A=
 *  Description: Adds an additional link to the complete list of =
languages available.=0A=
 *  Maintainers: [[User:AzaToth]], [[User:R. Koot]], [[User:Alex =
Smotrov]]=0A=
 */=0A=
=0A=
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'http://meta.wikimedia.org/wiki/List_of_Wikipedias',=0A=
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list of Wikipedias')=0A=
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)=0A=
=0A=
=0A=
/** Table sorting fixes ************************************************=0A=
  *=0A=
  *  Description: Disables code in table sorting routine to set classes =
on even/odd rows=0A=
  *  Maintainers: [[User:Random832]]=0A=
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=0A=
ts_alternate_row_colors =3D false;=0A=
=0A=
=0A=
/***** uploadwizard_newusers ********=0A=
 * Switches in a message for non-autoconfirmed users at =
[[Wikipedia:Upload]]=0A=
 *=0A=
 *  Maintainers: [[User:Krimpet]]=0A=
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function uploadwizard_newusers() {=0A=
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}=0A=
addOnloadHook(uploadwizard_newusers);=0A=
=0A=
=0A=
/** IPv6 AAAA connectivity testing **/=0A=
=0A=
var __ipv6wwwtest_factor =3D 100;=0A=
var __ipv6wwwtest_done =3D 0;=0A=
if ((wgServer !=3D "https://secure.wikimedia.org") && =
(Math.floor(Math.random()*__ipv6wwwtest_factor)=3D=3D42)) {=0A=
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}=0A=
=0A=
/** Magic editintros ****************************************************=0A=
 *=0A=
 *  Description: Adds editintros on disambiguation pages and BLP pages.=0A=
 *  Maintainers: [[User:RockMFR]]=0A=
 */=0A=
=0A=
function addEditIntro(name)=0A=
{=0A=
  var el =3D document.getElementById('ca-edit');=0A=
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}=0A=
=0A=
=0A=
if (wgNamespaceNumber =3D=3D 0) {=0A=
  addOnloadHook(function(){=0A=
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=0A=
  addOnloadHook(function(){=0A=
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    cats =3D cats.getElementsByTagName('a');=0A=
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=3D=3D 'Category:Possibly living people') {=0A=
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        break;=0A=
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  });=0A=
}=0A=
=0A=
//</source>=0A=
=0A=
/* MediaWiki:Monobook.js */=0A=
/* <source lang=3Djavascript> */=0A=
/* Any JavaScript here will be loaded for users using the MonoBook skin =
*/=0A=
=0A=
/** Anon tips and donation banner **************************=0A=
  *=0A=
  *  Description: This implements an anon tips / donation banner. It =
includes a workaround for=0A=
  *               the Z-index bug found in Internet Explorer. It =
correctly places the anon notice=0A=
  *               on the page, even under IE6. See this Google search =
for more information about the bug:=0A=
  *               http://www.google.com/search?q=3Dz-index+ie6+bug=0A=
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=0A=
if(wgUserName =3D=3D null) addOnloadHook((function (){=0A=
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wiki_00&utm_medium=3Danon_donation_banner&utm_campaign=3Dspontaneous_dona=
tion" class=3D"extiw" title=3D"wikimedia:Fundraising"><b>continued =
donations</b></a> keep Wikipedia running!';=0A=
        message[1]=3D'<a =
href=3D"http://wikimediafoundation.org/wiki/Donate/Now/en?utm_source=3Den=
wiki_01&utm_medium=3Danon_donation_banner&utm_campaign=3Dspontaneous_dona=
tion" class=3D"extiw" title=3D"foundation:Fundraising"><b>Make a =
donation</b></a> to Wikipedia and give the gift of knowledge!';=0A=
        message[2]=3D'Wikipedia is sustained by people like you. Please =
<a =
href=3D"http://wikimediafoundation.org/wiki/Donate/Now/en?utm_source=3Den=
wiki_02&utm_medium=3Danon_donation_banner&utm_campaign=3Dspontaneous_dona=
tion" class=3D"extiw" title=3D"foundation:fundraising"><b>donate</b></a> =
today.';=0A=
        message[3]=3D'Help us improve Wikipedia by <a =
href=3D"http://wikimediafoundation.org/wiki/Donate/Now/en?utm_source=3Den=
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financially</b></a>.';=0A=
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href=3D"http://wikimediafoundation.org/wiki/Donate/Now/en?utm_source=3Den=
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tion" class=3D"extiw" title=3D"wikimedia:Fundraising"><b>support =
Wikipedia</b></a> by making a tax-deductible donation.'=0A=
        message[5]=3D'Help us provide free content to the world by <a =
href=3D"http://wikimediafoundation.org/wiki/Donate/Now/en?utm_source=3Den=
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        message[6]=3D'<a =
href=3D"http://en.wikipedia.org/wiki/Wikipedia:Researching_with_Wikipedia=
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href=3D"http://en.wikipedia.org/wiki/Wikipedia:Ten_things_you_may_not_kno=
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Wikipedia">Ten things you may not know about Wikipedia.</a>';=0A=
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href=3D"http://en.wikipedia.org/wiki/Wikipedia:Ten_things_you_may_not_kno=
w_about_images_on_Wikipedia" title=3D"Wikipedia:Ten things you may not =
know about images on Wikipedia">Ten things you may not know about images =
on Wikipedia.</a>';=0A=
        message[9]=3D'<a =
href=3D"http://en.wikipedia.org/wiki/Wikipedia:Citing_Wikipedia" =
title=3D"Wikipedia:Citing Wikipedia">Learn more about citing =
Wikipedia.</a>';=0A=
        message[10]=3D'Have questions? <a =
href=3D"http://en.wikipedia.org/wiki/Wikipedia:Questions" =
title=3D"Wikipedia:Questions">Find out how to ask questions and get =
answers.</a>';=0A=
        message[11]=3D'<a =
href=3D"http://en.wikipedia.org/wiki/Wikipedia:Basic_navigation" =
title=3D"Wikipedia:Basic navigation">Find out more about navigating =
Wikipedia and finding information.</a>';=0A=
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href=3D"http://en.wikipedia.org/wiki/Wikipedia:Contributing_to_Wikipedia"=
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/** Topbar content fix with sitenotice / CentralNotice =
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  *  Description: This fixes the location of topbar content (e.g., =
featured=0A=
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active.=0A=
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------=_NextPart_000_0049_01CA353D.AD380F90--
