Power set

In mathematics, the power set of a set S, written as $P(S)$ or ${\mathcal {P}}(S)$ ,^[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 $P(S)$ would have $2^{n}$ elements.^[2]^[3]

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

References

↑ "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.

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[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.

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