# 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.