Definition:Ordering on Natural Numbers/Peano Structure

Definition
Let $\left({P, 0, s}\right)$ 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 $\left({P, 0, s}\right)$.