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• Axiom of choice
  In [[mathematics]], the '''Axiom of Choice''' or '''AC''' is a fundamental principle in [[set theory]] which states t There are a number of statements equivalent to the Axiom of Choice.
  2 KB (266 words) - 13:28, 5 January 2013
• Axiom of Choice
  #REDIRECT [[Axiom of choice]]
  29 bytes (4 words) - 01:49, 12 February 2009
• Talk:Axiom of choice
  170 bytes (22 words) - 03:53, 25 November 2011
• Template:Axiom of choice/Metadata
  | pagename = Axiom of choice | abc = Axiom of choice
  2 KB (228 words) - 01:50, 12 February 2009
• Axiom of choice/Definition
  182 bytes (30 words) - 08:45, 27 November 2011
• Axiom of choice/Bibliography
  620 bytes (76 words) - 13:07, 5 January 2013
• Axiom of choice/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Axiom of choice]]. Needs checking by a human.
  556 bytes (74 words) - 11:11, 11 January 2010

Page text matches

• Axiom of Choice
  #REDIRECT [[Axiom of choice]]
  29 bytes (4 words) - 01:49, 12 February 2009
• Axiom of choice
  In [[mathematics]], the '''Axiom of Choice''' or '''AC''' is a fundamental principle in [[set theory]] which states t There are a number of statements equivalent to the Axiom of Choice.
  2 KB (266 words) - 13:28, 5 January 2013
• Set theory/Related Articles
  {{r|Axiom of choice}}
  477 bytes (65 words) - 07:22, 22 July 2011
• Zermelo-Fraenkel axioms
  If to these is added the axiom of choice, the theory is designated as the ZFC theory:<ref name=Bell/> *9. <u>Axiom of choice</u>: Every family of nonempty sets has a choice function
  3 KB (512 words) - 17:28, 2 July 2011
• Cardinal number/Related Articles
  {{r|Axiom of choice}}
  370 bytes (47 words) - 17:50, 26 June 2009
• Template:Axiom of choice/Metadata
  | pagename = Axiom of choice | abc = Axiom of choice
  2 KB (228 words) - 01:50, 12 February 2009
• Axiom of choice/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Axiom of choice]]. Needs checking by a human.
  556 bytes (74 words) - 11:11, 11 January 2010
• Kurt Gödel/Related Articles
  {{r|Axiom of choice}}
  589 bytes (80 words) - 17:55, 11 January 2010
• Surjective function
  ...''f'' has an inverse <math>f^{-1}</math> (this requires us to assume the [[Axiom of Choice]]). If ''y'' is an element of the image set of ''f'', then there is at lea
  710 bytes (120 words) - 13:08, 13 November 2008
• Cartesian product/Related Articles
  {{r|Axiom of Choice}}
  927 bytes (149 words) - 02:35, 3 November 2008
• Cardinal number
  ...l [[rank (set theory)|rank]] equinumerous with ''X'' can be used. If the [[axiom of choice]] is available, ''X'' can always be well ordered, and |''X''| can be define ...r from ''Y'' to ''X'' without ''X'' and ''Y'' being equinumerous. With the axiom of choice however, the two relations are the same, and are a well ordering of the ca
  11 KB (1,808 words) - 17:50, 26 June 2009
• Talk:Irrational number
  ...at of the reals and greater than that of the rationals. If you accept the axiom of choice, then that's greater than aleph₁. As to what they ''are'', that ...t all elementary to prove. It is readily shown (if you allow yourself the axiom of choice) that the cardinality of the set of irrational nunmbers is ''at least'' <ma
  4 KB (694 words) - 21:24, 3 November 2007
• Vitali set
  ...ned by a particular mathematical construction. The construction uses the [[axiom of choice]] and its result given by an existence theorem is not uniquely determined. ...elds a partition of the set of reals into its equivalence classes. By the axiom of choice we can select a representative of each single class. The Vitali set ''V'' i
  4 KB (618 words) - 21:07, 15 November 2007
• Oxford University Press/Related Articles
  {{r|Axiom of choice}}
  1 KB (187 words) - 19:18, 11 January 2010
• Talk:Mathematical induction
  ...valence should be mentioned somewhere, if the explanation is given on the "axiom of choice" page.[[User:Barry R. Smith|Barry R. Smith]] 10:49, 6 April 2008 (CDT)
  4 KB (577 words) - 10:49, 6 April 2008
• Continuum hypothesis/Bibliography
  <br> Kurt Gödel, ''The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis''. (''The consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory''
  4 KB (568 words) - 15:50, 14 July 2009
• Schröder-Bernstein theorem
  ...heoretical interest that the proof of the theorem does not depend on the [[Axiom of Choice]]. </onlyinclude> and therefore (implicitly) relying on the Axiom of Choice.
  8 KB (1,281 words) - 15:39, 23 September 2013
• Schröder-Bernstein theorem/Citable Version
  ...heoretical interest that the proof of the theorem does not depend on the [[Axiom of Choice]]. and therefore (implicitly) relying on the Axiom of Choice.
  8 KB (1,275 words) - 15:34, 23 September 2013
• Set theory
  ...The resulting set theory, called ZF -- sometimes with the addition of the Axiom of Choice (ZFC); see below - has proved to be sufficient for the needs of much of mat If to these is added the axiom of choice, the theory is designated as the ZFC theory:
  24 KB (4,193 words) - 15:48, 23 September 2013
• Kurt Gödel
  ...org Cantor]]'s puzzling [[Continuum Hypothesis]] was consistent with the [[Axiom of Choice]], and that both were consistent with the [[Zermelo-Fraenkel axioms]]. This
  3 KB (375 words) - 15:26, 11 May 2011