In
mathematics, the
axiom of choice, or
AC, is an
axiom of
set theory equivalent to the statement that
the Cartesian product of a collection of non-empty sets is non-empty. 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.