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:
“High treason, when it is resistance to tyranny here below, has its origin in, and is first committed by, the power that makes and forever re-creates man.”
—Henry David Thoreau (1817–1862)
“Who set this ancient quarrel new abroach?”
—William Shakespeare (1564–1616)