 Axiom of power set

For every set $x$ there is a set $\mathcal{P}(x)$ whose members are exactly the subsets of $x$.

The Axiom of Power Set is one of the axioms in set theory, specifically within the Zermelo-Fraenkel set theory (ZF), which is a foundational system for much of modern mathematics. The axiom states that for any set \( A \), there exists a set \( P(A) \), called the power set of \( A \), which contains all the subsets of \( A \).