In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that "the product of a collection of non-empty sets is non-empty". More explicitly, it states that for every indexed family (S_i)_{i \in I} of nonempty sets there exists an indexed family (x_i)_{i \in I} of elements such that x_i \in S_i for every i \in I.