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.