# 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 2^{S}, 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

- ↑ Devlin (1979) p.50