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Answer by Atticus Stonestrom for Decide whether $\{ x | x=x\times x\}$ is a set

You are absolutely correct that it suffices to show that, for any $X$, if $X\neq\varnothing$ then $X\times X\neq X$. To see this, suppose for contradiction that $X$ is non-empty and equal to its...

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Decide whether $\{ x | x=x\times x\}$ is a set

This is an exercise my set theory teacher suggested we try and I feel like the answer is yes (because it seems to me that no set other than $\emptyset$ satisfies $x\times x=x$, then the collection...

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