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:
“The dignity and stability of government in all its branches, the morals of the people, and every blessing of society, depend so much upon an upright and skilful administration of justice, that the judicial power ought to be distinct from both the legislative and executive, and independent upon both, that so it may be a check upon both, as both should be checks upon that.”
—Thomas Jefferson (1743–1826)
“The ladies understood each other, in the careful way that ladies do once they understand each other. They were rather a pair than a couple, supporting each other from day to day, rather a set of utile, if ill-matched, bookends between which stood the opinion and idea in the metaphorical volumes that both connected them and kept them apart.”
—Alexander Theroux (b. 1940)