Definition:Trivial Ordering

Theorem

The trivial ordering is an ordering $\RR$ defined on a set $S$ by:

$\forall a, b \in S: a \mathrel \RR b \iff a = b$

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

Also see

• Trivial Ordering is Universally Compatible

Sources

• 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $\S 3.1$: Partially ordered sets: Example $1$