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 importance of a lost romantic vision should not be underestimated. In such a vision is power as well as joy. In it is meaning. Life is flat, barren, zestless, if one can find one’s lost vision nowhere.”
—Sarah Patton Boyle, U.S. civil rights activist and author. The Desegregated Heart, part 1, ch. 19 (1962)
“There are twenty ways of going to a point, and one is the shortest; but set out at once on one. A man who has that presence of mind which can bring to him on the instant all he knows, is worth for action a dozen men who know as much, but can only bring it to light slowly.”
—Ralph Waldo Emerson (1803–1882)