# Definition:Natural Numbers/Zermelo Construction/Historical Note

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## Historical Note on Zermelo Construction of Natural Numbers

The Zermelo construction of natural numbers was devised by Ernst Friedrich Ferdinand Zermelo.

While the approach is simple, it does not generalize easily to transfinite ordinals.

As a result, it is generally considered inferior to the von Neumann construction, which has considerable advantages over it.

Hence this approach is rarely seen, and noted for historical reasons only.

## Sources

- 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 1$ Preliminaries