Definition:Usual Ordering

Definition
Let $X$ be one of the sets of numbers: $\N$, $\Z$, $\Q$, $\R$.

The usual ordering on $X$ is the conventional counting and measuring order on $X$ that is learned when one is initially introduced to numbers.

Also known as
The usual ordering is also known as the natural ordering.

Also see

 * Ordered Integral Domain is Totally Ordered Ring, indicating that the usual ordering is a total ordering as required.


 * Complex Numbers cannot be Ordered Compatibly with Ring Structure, which demonstrates that $\C$ does not have a usual ordering.