# Difference between revisions of "Axiom of choice"

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The ''axiom of choice'' is an axiom, usually adjoined to the Zermelo-Frenkael axioms of set theory. Informally the axiom of choice says that given a family of non-empty sets we have a function selecting exactly one element from each set. The axiom is equivalent to the assertion that every set can be well ordered, and equivalently that all the infinite cardinals are [[Aleph|$\aleph$-numbers]]. | The ''axiom of choice'' is an axiom, usually adjoined to the Zermelo-Frenkael axioms of set theory. Informally the axiom of choice says that given a family of non-empty sets we have a function selecting exactly one element from each set. The axiom is equivalent to the assertion that every set can be well ordered, and equivalently that all the infinite cardinals are [[Aleph|$\aleph$-numbers]]. | ||

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## Revision as of 04:34, 5 January 2012

The *axiom of choice* is an axiom, usually adjoined to the Zermelo-Frenkael axioms of set theory. Informally the axiom of choice says that given a family of non-empty sets we have a function selecting exactly one element from each set. The axiom is equivalent to the assertion that every set can be well ordered, and equivalently that all the infinite cardinals are $\aleph$-numbers.

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