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:
“Great is Truth, and mighty above all things.”
—Apocrypha. 1 Esdras, 4:41.
Acclamation following the speech of the bodyguard of King Darius, who proclaimed the power of truth, “the strength, kingdom, power, and majesty of all ages.”
“Freedom is slavery some poets tell us.
Enslave yourself to the right leader’s truth,
Christ’s or Karl Marx’, and it will set you free.”
—Robert Frost (1874–1963)