nLab
comparison

A comparison on a set $A$ is a (binary) relation $\sim$ on $A$ such that in every pair of related elements, any other element is related to one of the original elements in the same order as the original pair:

$$\forall (x,y,z:A),x\sim z\Rightarrow x\sim y\vee y\sim z$$\forall (x, y, z: A),\; x \sim z \;\Rightarrow\; x \sim y \;\vee\; y \sim z

which generalises from $3$ to any (finite, positive) number of elements. To include the case where $n=0$, we must explicitly state that the relation is irreflexive.

Comparisons are most often studied in constructive mathematics. In particular, the relation $<$ on the (located Dedekind) real numbers is a comparison, even though its negation $\ge$ is not constructively total. (Indeed, $<$ is a linear order, even though $\ge$ is not constructively a total order.)