High Quality Content by WIKIPEDIA articles! 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 of nonempty sets there exists an indexed family of elements such that for every . The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem.