Axiom:Axiom of Infinity/Class Theory/Formulation 3

Axiom

Not every set is a natural number.

Also see

• Equivalence of Formulations of Axiom of Infinity for Zermelo Universe

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.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 2$ Definition of the Natural Numbers