I understand that the axiom of choice, given the axioms of ZF set theory, is equivalent to the statement that "the Cartesian product of any family of nonempty sets is nonempty." I've been unable to find this proof. Could someone sketch it for me? Or provide me with a source at least?
The Axiom of Choice and the Cartesian Product.
14
$\begingroup$
elementary-set-theory
axiom-of-choice
-
3This only depends on how you formulate the axiom of choice. – 2012-01-21