Axiom Of Choice

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The Axiom of Choice is an axiom of set theory, and states:

From any collection of disjoint, non-empty sets, $A_i,\quad~i=0,\;1,\;\ldots$ there is a set C containing one element from each $A_i$

This is slightly controversial, because it is non-constructive. It asserts the existence of the set C without telling you how to construct it.

The Axiom of Choice is equivalent to Zorn's Lemma and the Well-Ordering Principle.