Definition:Strict Ordering on Integers/Definition 1

Definition
The integers are strictly ordered on the relation $<$ as follows:


 * $\forall x, y \in \Z: x < y \iff y - x \in \Z_{>0}$

That is, $x$ is less than $y$ $y - x$ is (strictly) positive.

Also see

 * Equivalence of Definitions of Strict Ordering on Integers