Power set axiom

In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory.

In the formal language of the Zermelo–Fraenkel axioms, the axiom reads:

where y is the Power set of x, ${\displaystyle {\mathcal {P}}(x)}$. In English, this says:

More succinctly: for every set ${\displaystyle x}$, there is a set ${\displaystyle {\mathcal {P}}(x)}$ consisting precisely of the subsets of ${\displaystyle x}$.

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