# Axiom of choice

The **Axiom of choice** is an axiom of set theory. The axiom of choice says that if one is given any collection of boxes, each containing at least one object, it is possible to make a selection of exactly one object from each box, even if the collection is infinite.

Formally, the Axiom of choice says that, given a non-empty set of non-empty sets, there is a choice function on . That is, there is a function such that for each . It is also equivalent to the statement that, given a set of non-empty sets, is non-empty. An equivalent form of the Axiom of choice says, given a set of non-empty pairwise disjoint sets, there exists a set with one element from each set in .

The Axiom of choice is equivalent to Zorn's Lemma and the Well-Ordering theorem assuming Zermelo-Fraenkel Axioms.

It was discovered by German mathematician, Ernst Zermelo in 1904.

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