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:
“The power of a text is different when it is read from when it is copied out.... Only the copied text thus commands the soul of him who is occupied with it, whereas the mere reader never discovers the new aspects of his inner self that are opened by the text, that road cut through the interior jungle forever closing behind it: because the reader follows the movement of his mind in the free flight of day-dreaming, whereas the copier submits it to command.”
—Walter Benjamin (1892–1940)
“Freedom is slavery some poets tell us.
Enslave yourself to the right leader’s truth,
Christ’s or Karl Marx’, and it will set you free.”
—Robert Frost (1874–1963)