Axiom of power set

Concept in axiomatic set theory

In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory. It guarantees for every set x {\displaystyle x} the existence of a set P ( x) {\displaystyle {\mathcal {P}}(x)} , the power set of x {\displaystyle x} , consisting precisely of the subsets of x {\displaystyle x} . By the axiom of extensionality, the set P ( x) {\displaystyle {\mathcal {P}}(x)} is unique.

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