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:
“Just as children, step by step, must separate from their parents, we will have to separate from them. And we will probably suffer...from some degree of separation anxiety: because separation ends sweet symbiosis. Because separation reduces our power and control. Because separation makes us feel less needed, less important. And because separation exposes our children to danger.”
—Judith Viorst (20th century)
“But at the coming of the King of Heaven
All’s set at six and seven:
We wallow in our sin;
Christ cannot finde a chamber in the inn.”
—Unknown. Yet if His Majesty, Our Sovereign Lord (l. 25–28)