Russel's Paradox

aka barber paradox

russel's paradox states that one cannot construct the set of all sets that don't contain themselves, and thus one cannot construct the set of all sets --- https://youtu.be/I8LbkfSSR58?t=1559

if \(S = \{x : x \notin x\}\), is \(S \in S\)?. set-builder notation obscures the contradiction but writing the equivalent \(x \in S = x \notin x\) reveals it