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 $y$ if and only if $y - x$ is (strictly) positive.

Also see

• Equivalence of Definitions of Strict Ordering on Integers

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $2$: Ordered and Well-Ordered Integral Domains: $\S 7$. Order