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:
“To take pride in a library kills it. Then, its motive power shifts over to the critical if admiring visitor, and apologies are necessary and acceptable and the fat is in the fire.”
—Carolyn Wells (1862–1942)
“Old people love to give good advice to console themselves for no longer being able to set a bad example.”
—François, Duc De La Rochefoucauld (1613–1680)