Definition:Total Ordering/Class Theory

Definition
Let $V$ be a basic universe.

Let $\RR \subseteq V \times V$ be a relation.

Let $\RR$ be such that:


 * $(1): \quad \RR$ is an ordering on $\Field \RR$
 * $(2): \quad \forall x, y \in \Field \RR: x \mathop \RR y \lor y \mathop \RR x$ (that is, $x$ and $y$ are comparable)

where $\Field \RR$ denotes the field of $\RR$.

Then $\RR$ is a total ordering.

Also see

 * Definition:Totally Ordered Class