Axiom:Axiom of Choice/Formulation 1

Axiom
For every set of non-empty sets, we can provide a mechanism for choosing one element of each element of the set.


 * $\displaystyle \forall s: \paren {\O \notin s \implies \exists \paren {f: s \to \bigcup s}: \forall t \in s: \map f t \in t}$

That is, one can always create a choice function for selecting one element from each element of the set.

Also see

 * Equivalence of Versions of Axiom of Choice