Power set

In mathematics, the power set of a set S, written as $P(S)$ or $𝒫(S)$, 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 $P(S)$ would have $2^n$ elements.

Examples

• The power set of $\{2,5\}$ is $\{\{\},\{2\},\{5\},\{2,5\}\}$.
• The power set of $\{3,4,10\}$ is $\{\{\},\{3\},\{4\},\{10\},\{3,4\},\{3,10\},\{4,10\},\{3,4,10\}\}$.

Related pages

• Zermelo–Fraenkel set theory, which includes an axiom on power set