Definition:Ordering on Integers/Definition 1
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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.
- 1994: H.E. Rose: A Course in Number Theory (2nd ed.) ... (previous) ... (next): $1$ Divisibility: $1.1$ The Euclidean algorithm and unique factorization