A power set of S is the set of all subsets of S, usually represented as 𝒫(*S*), *P*(*S*), ℙ(S). Given S is a finite set, the cardinality is n, represented as `|S| = n`

. The cardinality of `|P(S)| = 2^n`

.

`|P(S)| > |S|`

always have higher cardinality than, as proven with Cantor's diagonal argument. For infinite sets this holds, for example given `S`

is countably infinite, `P(S)`

is uncountably infinity.