# Definition:Ordering on Integers/Definition 1

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## Definition

The integers are ordered on the relation $\le$ as follows:

$\forall x, y \in \Z: x \le y$
$\exists c \in P: x + c = y$

where $P$ is the set of positive integers.

That is, $x$ is less than or equal to $y$ if and only if $y - x$ is non-negative.