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

• From any collection of disjoint, non-empty sets, $A_i,~i\in{I},$
• 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.

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AxiomOfChoice
Axiom
PartiallyOrderedSet
UncountableSet
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EuclideanGeometry
KurtGoedel
PoincaresDisc