Power set

Power set

The elements of the power set of {x, y, z} ordered with respect to inclusion.
Type	Set operation
Field	Set theory
Statement	The power set is the set that contains all subsets of a given set.
Symbolic statement	${\displaystyle x\in P(S)\iff x\subseteq S}$

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.^[1] 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.^[2] The powerset of S is variously denoted as P(S), 𝒫(S), P(S), ${\displaystyle \mathbb {P} (S)}$, ${\displaystyle \wp (S)}$, or 2^S.^[a] Any subset of P(S) is called a family of sets over S.

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