Power set
In mathematics, the power set of a set S, written as <math>P(S)</math> or <math>\mathcal{P}(S)</math>,[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 <math>P(S)</math> would have <math>2^n</math> elements.[2][3]
Examples[change]
- The power set of <math>\{2, 5\}</math> is <math>\{\{\}, \{2\}, \{5\}, \{2, 5\}\}</math>.
- The power set of <math>\{3, 4, 10\}</math> is <math>\{\{\}, \{3\}, \{4\}, \{10\}, \{3, 4\}, \{3, 10\}, \{4, 10\}, \{3, 4, 10\}\}</math>.
Related pages[change]
- Zermelo–Fraenkel set theory, which includes an axiom on power set
References[change]
- ↑ "Comprehensive List of Set Theory Symbols". Math Vault. 2020-04-11. Retrieved 2020-09-05.
- ↑ Weisstein, Eric W. "Power Set". mathworld.wolfram.com. Retrieved 2020-09-05.
- ↑ "Power Set". www.mathsisfun.com. Retrieved 2020-09-05.
