Definition:Power Set

The power set of a set $$S$$, denoted $$\mathcal{P} \left({S}\right)$$, is the set defined as follows:

$$\mathcal{P} \left({S}\right) = \left\{ {T: T \subseteq S}\right\}$$

That is, the set whose elements are all of the subsets of $$S$$.

Note that this is a set all of whose elements are themselves sets.

There are alternative notations for this, e.g.:


 * $$\mathfrak {P} \left({S}\right)$$;
 * $$2^S$$.