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:
“Of a truth, Knowledge is power, but it is a power reined by scruple, having a conscience of what must be and what may be; whereas Ignorance is a blind giant who, let him but wax unbound, would make it a sport to seize the pillars that hold up the long- wrought fabric of human good, and turn all the places of joy as dark as a buried Babylon.”
—George Eliot [Mary Ann (or Marian)
“If we cannot find a way to interpret the utterances and other behaviour of a creature as revealing a set of beliefs largely consistent and true by our own standards, we have no reason to count that creature as rational, as having beliefs, or as saying anything.”
—Donald Davidson (b. 1917)