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:
“It does not follow ... that the right to criticize Shakespeare involves the power of writing better plays. And in fact—do not be surprised at my modesty—I do not profess to write better plays.”
—George Bernard Shaw (1856–1950)
“All I’m telling you is that that little creature in there has as much right to live as you do. Don’t forget, you invaded his world. You sank a pipe six miles into the ground and when he climbed up you set dogs on him, shot him.”
—Richard Fielding, and Lee Sholem. Superman (George Reeves)