Axiom:Axiom of Infinity/Class Theory/Formulation 3

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Not every set is a natural number.

Also see

Historical Note

Raymond M. Smullyan and Melvin Fitting introduce this formulation of the Axiom of Infinity in their Set Theory and the Continuum Problem, Revised ed. of $2010$ as:

something rather amusing.

It would not normally be expected that this formulation be used as the basis of serious work in this field of mathematics.