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:
“Purchasing power is a license to purchase power.”
—Raoul Vaneigem (b. 1934)
“They roused him with muffins—they roused him with ice—
They roused him with mustard and cress—
They roused him with jam and judicious advice—
They set him conundrums to guess.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)