No Bijection from Set to its Power Set

Theorem
Let $S$ be a set, and let $\mathcal P \left({S}\right)$ be its power set.

There is no bijection $f: S \to \mathcal P \left({S}\right)$.

Proof
A bijection is by its definition also a surjection.

By Cantor's Theorem there is no surjection from $S$ to $\mathcal P \left({S}\right)$.

Hence the result.