Power set

In mathematics, the power set of a set S, written as ${\displaystyle P(S)}$ or ${\displaystyle {\mathcal {P}}(S)}$,[1] 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.[2][3]

Examples

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

References

1. "Comprehensive List of Set Theory Symbols". Math Vault. 2020-04-11. Retrieved 2020-09-05.
2. Weisstein, Eric W. "Power Set". mathworld.wolfram.com. Retrieved 2020-09-05.
3. "Power Set". www.mathsisfun.com. Retrieved 2020-09-05.