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:
“Power corrupts ... when the weak band together in order to ruin the strong, but not before. The will to power ... far from being a characteristic of the strong, is, like envy and greed, among the vices of the weak, and possibly even their most dangerous one.”
—Hannah Arendt (1906–1975)
“It is a great pity—but ‘tis certain from every day’s observation of man, that he may be set on fire like a candle, at either end—provided there is a sufficient wick standing out.”
—Laurence Sterne (1713–1768)