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:
“The tendency of things runs steadily to this point, namely, to put every man on his merits, and to give him so much power as he naturally exerts,—no more, no less.”
—Ralph Waldo Emerson (1803–1882)
“I set it down as a fact that if all men knew what each said of the other, there would not be four friends in the world.”
—Blaise Pascal (1623–1662)