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:
“Armies, though always the supporters and tools of absolute power for the time being, are always the destroyers of it too; by frequently changing the hands in which they think proper to lodge it.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Really, if the lower orders don’t set us a good example, what on earth is the use of them? They seem, as a class, to have absolutely no sense of moral responsibility.”
—Oscar Wilde (1854–1900)