Is a set containing itself already a paradox?How is it so?


 I can't understand how is Russel's paradox really a paradox if a set containing itself isn't. Am I missing something? Is this issue recognized and if so how is it dealt with?

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1 Answer

In modern set theory (read: ZFC) there is no such set. The axiom of foundation ensures that such sets do not exist, which means that the class defined by Russell in the paradox is in fact the collection of all sets.
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