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:
“He who knows that power is inborn, that he is weak because he has looked for good out of him and elsewhere, and, so perceiving, throws himself unhesitatingly on his thought, instantly rights himself, stands in the erect position, commands his limbs, works miracles; just as a man who stands on his feet is stronger than a man who stands on his head.”
—Ralph Waldo Emerson (1803–1882)
“We set this nation up ... to vindicate the rights of man. We did not name any differences between one race and another. We opened our gates to all the world and said: “Let all men who want to be free come to us and they will be welcome.””
—Woodrow Wilson (1856–1924)