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:
“Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintance with numbers will show the immensity of the first power in comparison of the second.”
—Thomas Robert Malthus (1766–1834)
“It is a great mistake to suppose that clever, imaginative children ... should content themselves with the empty nonsense which is so often set before them under the name of Children’s Tales. They want something much better; and it is surprising how much they see and appreciate which escapes a good, honest, well- informed papa.”
—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)