\begin{definition}[Definition:Ordering on Natural Numbers/Peano Structure]
Let $\struct {P, 0, s}$ be a Peano structure.
The '''ordering''' of $P$ is the relation $\le$ defined by:
:$\forall m, n \in P: m \le n \iff \exists p \in P: m + p = n$
where $+$ denotes addition in $\struct {P, 0, s}$.
\end{definition}