Power set

In mathematics, the power set of a set S, written as ${\displaystyle P(S)}$ or ${\displaystyle {\mathcal {P}}(S)}$, is the set of all subsets of S. In terms of cardinality, a power set is larger than the set it originates from. If S is a finite set with n elements, then ${\displaystyle P(S)}$ would have ${\displaystyle 2^{n}}$ elements.