# Russell's Paradoxes

Book: The Man from the Future: The Visionary Life of John von Neumann

Let $R$ be the set of all sets that are not members of themselves. If $R$ is not a member of itself, then its definition entails that it is a member of itself; if it is a member of itself, then it is not a member of itself.

$R = \{x | x \not\in x\}$

Then,

$R \in R \iff R \not\in R$