Definition:Total Ordering

Definition
Let $\mathcal R \subseteq S \times S$ be a relation on a set $S$.

Also known as
Some sources call this a linear ordering, or a simple ordering.

If it is necessary to emphasise that a total ordering $\preceq$ is not strict, then the term weak total ordering may be used.

Also see

 * Definition:Totally Ordered Set


 * Definition:Strict Total Ordering