Axiom of Choice

Pronunciation: /ˈæksiəm ʌv tʃɔɪs/ ?

The axiom of choice states that an infinite set, such as the set of all even integers, can be created from other infinite sets, such as the set of all integers[1][2]. This axiom enables mathematical proofs that require selecting a set from a larger set or collection of sets.

This axiom is sometimes called Zermelo's axiom of choice as it was formulated by Ernst Zermelo [German, 1871-1956] in 1904.

References

  1. Jech, Thomas. Set Theory. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. (Accessed: 2009-12-15). http://plato.stanford.edu/entries/set-theory/.
  2. Bell, John L.. The Axiom of Choice. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. (Accessed: 2009-12-16). http://plato.stanford.edu/entries/axiom-choice/.

More Information

  • McAdams, David. Axiom. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Axiom.
  • J J O'Connor and E F Robertson. Ernst Friedrich Ferdinand Zermelo. 2009-03-12. http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Zermelo.html.

Printed Resources

Cite this article as:


Axiom of Choice. 2008-04-23. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/axiomofchoice.html.

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2009-12-15: Added "References" (McAdams, David.)
2008-04-23: Initial version (McAdams, David.)

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