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 dissident does not operate in the realm of genuine power at all. He is not seeking power. He has no desire for office and does not gather votes. He does not attempt to charm the public, he offers nothing and promises nothing. He can offer, if anything, only his own skin—and he offers it solely because he has no other way of affirming the truth he stands for. His actions simply articulate his dignity as a citizen, regardless of the cost.”
—Václav Havel (b. 1936)
“Those who set out to serve both God and Mammon soon discover that there isn’t a God.”
—Logan Pearsall Smith (1865–1946)