For any two sets there is a set containing exactly those two members. Together with other ZFC axioms it permits ordinary ordered-pair coding. Countable-subset closure implies this axiom for the structure of hereditarily countable sets.
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The Axiom of Pairing is a fundamental concept in set theory, particularly in the context of Zermelo-Fraenkel set theory (ZF). It is one of the axioms that helps to establish the foundations for building sets and functions within mathematics. The Axiom of Pairing states that for any two sets \( A \) and \( B \), there exists a set \( C \) that contains exactly \( A \) and \( B \) as its elements.