Cantor's Theorem

Statement

Let $X$ be a set, $\mathcal{P}$ denote power set and $|\_|$ denote Cardinal, then $|\mathcal{P}X|>|X|$ In other words, there is a surjection, but no Injection from $\mathcal{P}X$ to $X$.

Proof

https://proofwiki.org/wiki/Cantor%27s_Theorem

Corolloray

There is no set $\mathcal{S}et$ of all sets, since the power set $|\mathcal{P}\mathcal{S}et|>|\mathcal{S}et|$, so it cannot be that $\mathcal{P}\mathcal{S}et\subset \mathcal{S}et$.