Power set

Mathematical set containing all subsets of a given set

In mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. The powerset of S is variously denoted as P(S), 𝒫(S), P(S), , , or 2S. Any subset of P(S) is called a family of sets over S.

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