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:
“Germany will either be a world power or will not be at all.”
—Adolf Hitler (1889–1945)
“No annual training or muster of soldiery, no celebration with its scarfs and banners, could import into the town a hundredth part of the annual splendor of our October. We have only to set the trees, or let them stand, and Nature will find the colored drapery,—flags of all her nations, some of whose private signals hardly the botanist can read,—while we walk under the triumphal arches of the elms.”
—Henry David Thoreau (1817–1862)