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https://en.wikipedia.org/wiki/Zermelo_set_theory
Zermelo set theory
The axioms of Zermelo set theory
The axioms of Zermelo set theory are stated for objects, some of which (but not necessarily all) are sets, and the remaining objects are urelements and not sets. Zermelo's language implicitly includes a membership relation ∈, an equality relation = (if it is not included in the underlying logic), and a unary predicate saying whether an object is a set. Later versions of set theory often assume that all objects are sets so there are no urelements and there is no need for the unary predicate.

7.AXIOM VII. Axiom of infinity (Axiom des Unendlichen) "There exists in the domain at least one set Z that contains the null set as an element and is so constituted that to each of its elements a there corresponds a further element of the form {a}, in other words, that with each of its elements a it also contains the corresponding set {a} as element."

Connection with standard set theory
The axiom of infinity is usually now modified to assert the existence of the first infinite von Neumann ordinal
ω; the original Zermelo axioms cannot prove the existence of this set, nor can the modified Zermelo axioms prove Zermelo's axiom of infinity.[2]
Zermelo's axioms (original or modified) cannot prove the existence of Vω as a set nor of any rank of the cumulative hierarchy of sets with infinite index. In any formulation, Zermelo set theory cannot prove the existence of the von Neumann ordinal ω·2, despite proving the existence of such an order type; thus the von Neumann definition of ordinals is not employed for Zermelo set theory.
Zermelo allowed for the existence of urelements that are not sets and contain no elements; these are now usually omitted from set theories.

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