The axiom of choice
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.
This article is a stub. Please help us to improve Cantor's Attic by adding information.