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:
“There is a power whose care
Teaches thy way along that pathless coast,—”
—William Cullen Bryant (1794–1878)
“What is love itself,
Even though it be the lightest of light love,
But dreams that hurry from beyond the world
To make low laughter more than meat and drink,
Though it but set us sighing?”
—William Butler Yeats (1865–1939)