Definition:Total Ordering/Class Theory

Definition
Let $V$ be a basic universe.

A total ordering in $V$ is a relation $\RR \subseteq V \times V$ such that:


 * $(1): \quad \RR$ is an ordering on $S$
 * $(2): \quad \RR$ is connected

That is, $\RR$ is an ordering such that all pairs of elements of $\Field \RR$ are comparable:


 * $\forall x, y \in \Field \RR: x \mathop \RR y \lor y \mathop \RR x$