Total Order

Overview

A binary relation $R$ on set $A$ is a non-strict total order on $A$ iff it is reflexive on $A$, antisymmetric, transitive, and strongly connected. In other words, a non-strict total order is a strongly connected partial order.

If instead $R$ is irreflexive on $A$ and connected, then $R$ is a strict total order on $A$. In other words, a strict total order is a connected strict partial order.