Power Set Operation
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A Power Set Operation is a Set Operation that produces a set whose Set Members are all the possible distinct Subsets of a set.
- AKA: PowerSet, Power Set, PS, Power Set Function.
- Example(s):
- PS({H,T})={{},{H},{T},{H,T}}.
- See: Set Measure Space, Sigma Field, Formal Language, Subset, Empty Set, Axiomatic Set Theory, ZFC, Axiom of Power Set, Family of Sets.
References
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Power_set Retrieved:2014-4-21.
- In mathematics, the power set (or powerset) of any set S, written [math]\displaystyle{ \mathcal{P}(S) }[/math], P(S), 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. [1]
Any subset of [math]\displaystyle{ \mathcal{P}(S) }[/math] is called a family of sets over S.
- In mathematics, the power set (or powerset) of any set S, written [math]\displaystyle{ \mathcal{P}(S) }[/math], P(S), 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. [1]
- ↑ Devlin (1979) p.50