Definition:Trivial Ordering

Theorem
The trivial ordering is an ordering $\mathcal R$ in a poset $\left({S, \mathcal R}\right)$ such that:


 * $\forall a, b \in S: a \mathrel{\mathcal R} b \iff a = b$

That is, there is no ordering defined on any two distinct elements of the set $S$.

Also see

 * Trivial Ordering is Universally Compatible