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:
“...I am who I am because I’m a black female.... When I was health director in Arkansas ... I could talk about teen-age pregnancy, about poverty, ignorance and enslavement and how the white power structure had imposed it—only because I was a black female. I mean, black people would have eaten up a white male who said what I did.”
—Joycelyn Elders (b. 1933)
“But beauty is set apart,
beauty is cast by the sea,
a barren rock,
beauty is set about
with wrecks of ships....”
—Hilda Doolittle (1886–1961)