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as an existent set on its own, or if Cantor merely used as an emptiness predicate. Zermelo accepted itself as a set, but considered it an "improper set".

Axiomatic set theory

In Zermelo set theory, the existence of the empty set is assured by the axiom of empty set, and its uniqueness follows from the axiom of extensionality. However, the axiom of empty set can be shown redundant in at

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