In mathematics, the power set (or powerset) of any set S, written, P(S), ℘(S) or 2S, 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.
Any subset of is called a family of sets over S.
Read more about Power Set: Example, Properties, Representing Subsets As Functions, Relation To Binomial Theorem, Algorithms, Subsets of Limited Cardinality, Topologization of Power Set, Power Object
Famous quotes containing the words power and/or set:
“What you fail to understand is the power of hate. It can fill the heart as surely as love can.”
—Earl Felton, and Richard Fleischer. Captain Nemo (James Mason)
“Those who set out to serve both God and Mammon soon discover that there isn’t a God.”
—Logan Pearsall Smith (1865–1946)