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 am willing, for a money consideration, to test this physical strength, this nervous force, and muscular power with which I’ve been gifted, to show that they will bear a certain strain. If I break down, if my brain gives way under want of sleep, my heart ceases to respond to the calls made on my circulatory system, or the surcharged veins of my extremities burst—if, in short, I fall helpless, or it may be, dead on the track, then I lose my money.”
—Ada Anderson (1860–?)
“I move my thin legs into your office
and we work over the cadaver of my soul.
We make a stage set out of my past
and stuff painted puppets into it.”
—Anne Sexton (1928–1974)