In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that "a Cartesian product of a collection of non-empty sets is non-empty". Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if the collection is infinite. Formally, it states that for every indexed family formula_1 of nonempty sets there exists an indexed family formula_2 of elements such that formula_3 for every formula_4. The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem.