Power Set

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.