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Does the set of all sets other than the empty set include the empty set?

In: Math and Arithmetic [Edit categories]

Answer:

The collection of all sets minus the empty set is not a set (it is too big to be a set) but instead a proper class. See Russell's paradox for why it would be problematic to consider this a set. According to axioms of standard ZFC set theory, not every intuitive "collection" of sets is a set; we must proceed carefully when reasoning about what is a set according to ZFC.

First answer by ID2147628271. Last edit by ID2147628271. Question popularity: 1 [recommend question].

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