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:
“Opinions have greater power than strength of hands.”
—Sophocles (497–406/5 B.C.)
“And set off briskly for so slow a thing,
Still going every which way in the joints, though,
So that it looked like lightning or a scribble.”
—Robert Frost (1874–1963)