Russell's Paradox

Definition

There is no set of all sets

Proof

Let $R=\{x|x\notin x\}$, then $R\in R\iff R\notin R$

Let $R$ be the set of all sets that are not members of themselves. If $R$ is not a member of itself, by the definition of itself, that is a member of itself; yet, if it is a member of itself, then it doesn’t satisfy its definition.