For every set , there is a set whose elements are exactly the elements of members of :

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The Axiom of Union is one of the axioms in set theory, particularly within the Zermelo-Fraenkel set theory (ZF), which is a foundational system for mathematics. The Axiom of Union states that for any set \( A \), there exists a set \( B \) that contains exactly the elements of the elements of \( A \).