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:
“I hate this shallow Americanism which hopes to get rich by credit, to get knowledge by raps on midnight tables, to learn the economy of the mind by phrenology, or skill without study, or mastery without apprenticeship, or the sale of goods through pretending that they sell, or power through making believe you are powerful, or through a packed jury or caucus, bribery and “repeating” votes, or wealth by fraud.”
—Ralph Waldo Emerson (1803–1882)
“[T]he dignity of parliament it seems can brook no opposition to it’s power. Strange that a set of men who have made sale of their virtue to the minister should yet talk of retaining dignity!”
—Thomas Jefferson (1743–1826)