Does this set exist? – math.stackexchange.com

Does this set exist? – math.stackexchange.com

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Consider the set $$S=\{x\mid x\in S\}.$$ For every element $x$, either $x\in S$ or $x\not\in S.$ If we know that $x$ is in fact element of $S$, then, by definition, $x\in S$ so it is true that $x\in ...

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