User:Dfeuer/Ordering on Natural Numbers/Peano

Definition
Let $\left({\N, 0, s}\right)$ be a Peano structure, where $\N$ is a set.

Let $<$ be the transitive closure of $s$.

Let $\le$ be the reflexive closure of $<$.

Then:


 * $<$ is the usual strict ordering of the natural numbers.


 * $\le$ is the usual ordering of the natural numbers.