Total Ordering is Total Relation
Jump to navigation Jump to search
Let $S$ be a set.
Let $\mathcal R \subseteq S \times S$ be a total ordering.
Then $\mathcal R$ is a total relation.
By definition of total ordering:
- $\mathcal R$ is a reflexive relation on the strength of being an ordering
- $\mathcal R$ is a connected relation on the strength of being a total ordering.