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:
“and men strive with each other not for power or the accumulation of paper
but in joy create for others the house, the poem, the game of
athletic beauty.
Then washed in the brightness of the vision,
I saw how in its radiance would grow and be nourished and suddenly
burst into terrible and splendid bloom
the blood-red flower of revolution.”
—Dudley Randall (b. 1914)
“yes, set fire to frostbitten crops,
drag out forgotten fruit
to dance the flame-tango,
the smoke-gavotte,
to live after all....”
—Denise Levertov (b. 1923)