Choice function

A choice function is a mathematical function <math>f<math> whose domain <math>X<math> is a collection of nonempty sets such that for every <math>S<math> in <math>X<math>, <math>f(S)<math> is in <math>S<math>. In other words <math>f<math> chooses exactly one element from each set in <math>X<math>.

The Axiom of Choice is often stated in terms of a choice function: "For every collection <math>X<math> of nonempty sets, there exists a choice function on <math>X<math>."