Power set
In mathematics, the power set of a set S, written as [math]\displaystyle{ P(S) }[/math] or [math]\displaystyle{ \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]\displaystyle{ P(S) }[/math] would have [math]\displaystyle{ 2^n }[/math] elements.[2][3]
Examples
- The power set of [math]\displaystyle{ \{2, 5\} }[/math] is [math]\displaystyle{ \{\{\}, \{2\}, \{5\}, \{2, 5\}\} }[/math].
- The power set of [math]\displaystyle{ \{3, 4, 10\} }[/math] is [math]\displaystyle{ \{\{\}, \{3\}, \{4\}, \{10\}, \{3, 4\}, \{3, 10\}, \{4, 10\}, \{3, 4, 10\}\} }[/math].
Related pages
- Zermelo–Fraenkel set theory, which includes an axiom on power set