Russell's paradox

Description:

• A set defined as $R=\{S|S\notin S\}$:
  • R is set of all sets, S, that dont contain themself as an element
• is R a set? R is not a set or a collection
• $S\in \{x|x\in U,...\}$ is always a set where $U=E\cup \mathcal{P}(E)\cup \mathcal{P}(\mathcal{P}(E))\cup ...$ but we only care a set as a subset of $U$