Power set

Power set
The elements of the power set of {x, y, z} ordered with respect to inclusion.
TypeSet operation
FieldSet theory
StatementThe power set is the set that contains all subsets of a given set.
Symbolic statement

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), , or 2S.[a] Any subset of P(S) is called a family of sets over S.

  1. ^ a b Weisstein
  2. ^ Devlin 1979, p. 50


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