Cantor's Paradox

Definition

There is no greatest cardinal number

There is no set of all sets

Proof

Let $U$ be the set of all sets and its cardinal number be $k$ Then, by the Cantor’s Theorem, $|\mathcal{P}(U)|=2^k>k=|U|$. It is contradicted to the assumption $|U|\ge |\mathcal{P}(X)|$