\begin{definition}[Definition:Ordering on Integers/Definition 1]
The integers are ordered on the relation $\le$ as follows:
:$\forall x, y \in \Z: x \le y$
{{iff}}:
:$\exists c \in P: x + c = y$
where $P$ is the set of positive integers.
That is, $x$ is '''less than or equal''' to $y$ {{iff}} $y - x$ is non-negative.
\end{definition}