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:
“Nature has given women so much power that the law has very wisely given them little.”
—Samuel Johnson (1709–1784)
“Stories of law violations are weighed on a different set of scales in the Black mind than in the white. Petty crimes embarrass the community and many people wistfully wonder why Negroes don’t rob more banks, embezzle more funds and employ graft in the unions.... This ... appeals particularly to one who is unable to compete legally with his fellow citizens.”
—Maya Angelou (b. 1928)