Mathematical set containing all subsets of a given set
For the search engine developer, see Powerset (company).
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
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.
^ abWeisstein
^Devlin 1979, p. 50
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mathematics, the powerset (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...
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set of subsets of a given set (its powerset) ordered by inclusion (see Fig. 1). Similarly, the set of sequences ordered by subsequence, and the set of...
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