Peano axioms

The Peano Axioms can be used to describe the set of natural numbers, ω, as part of the ordinal numbers (Ordinal).

Specifically, they are:

1. Zero is in ω.
2. For all n, if n is in ω, then (n+1) is in ω.
3. For all n and for all m, if n is not equal to m, then (n+1) is not equal to (m+1).
4. For all X, if X is a subset of ω, X contains Zero, and if for all n in X, X also contains (n+1), then X is equal to ω.