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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
• 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
• 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
• 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
• 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
• Cartesian product
  The [[Axiom of Choice]] is equivalent to stating that a product of any family of non-empty sets i
  3 KB (440 words) - 12:26, 30 December 2008
• Continuum hypothesis
  who showed that &ndash; in set theory including the [[axiom of choice]] &ndash; But since &ndash; in contrast to the situation with the axiom of choice &ndash;
  8 KB (1,289 words) - 20:20, 15 July 2009
• Set theory/Citable Version
  ...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 === The axiom of choice ===
  22 KB (3,815 words) - 15:46, 23 September 2013