Axiom of Choice
Pronunciation: /ˈæk.si.əm ʌv tʃɔɪs/ Explain
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
- McAdams, David E.. All Math Words Dictionary, axiom of choice. 2nd Classroom edition 20150108-4799968. pg 23. Life is a Story Problem LLC. January 8, 2015. Buy the book
- Jech, Thomas. Set Theory. 3rd edition. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. Last Accessed 6/12/2018. http://plato.stanford.edu/entries/set-theory. Buy the book
- Bell, John L.. The Axiom of Choice. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. Last Accessed 6/12/2018. http://plato.stanford.edu/entries/axiom-choice.
More Information
- Eric Schechter. Axiom of Choice. math.vanderbilt.edu. Vanderbilt University. 6/19/2018. https://math.vanderbilt.edu/schectex/ccc/choice.html.
- McAdams, David E.. Axiom. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/19/2018. http://www.allmathwords.org/en/a/axiom.html.
Cite this article as:
McAdams, David E. Axiom of Choice. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/axiomofchoice.html.
Revision History
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
6/15/2018: Removed broken links, updated license, implemented new markup. (
McAdams, David E.)
12/15/2009: Added "References". (
McAdams, David E.)
4/23/2008: Initial version. (
McAdams, David E.)