Power set
Mathematical set containing all subsets of a given set / From Wikipedia, the free encyclopedia
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For the search engine developer, see Powerset (company).
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.[lower-alpha 1] Any subset of P(S) is called a family of sets over S.
Quick Facts Type, Field ...
Type | Set operation |
---|---|
Field | Set theory |
Statement | The power set is the set that contains all subsets of a given set. |
Symbolic statement |
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