Definition:Ordering on Integers/Definition 1

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


 * $\forall x, y \in \Z: x \le y$


 * $\exists c \in P: x + c = y$
 * $\exists c \in P: x + c = y$

where $P$ is the set of positive integers.

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

Also see

 * Equivalence of Definitions of Ordering on Integers


 * Definition:Strict Ordering on Integers


 * Definition:Ordering on Natural Numbers