Axiom of union

In axiomatic set theory, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory. This axiom was introduced by Ernst Zermelo.

Informally, the axiom states that if ⁠⁠ is a set of sets, then the union of all sets in ⁠⁠ is still a set. In more basic terms, for each set ⁠⁠ there is a set ⁠⁠ whose elements are precisely the elements of the elements of ⁠⁠.

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