The latter are reflexive, transitive, and total relations over the set of models.

However, if R and S are total relations, T is in general not.

Total relations are sometimes said to have comparability.

Total relations ('all the concrete collections inherit from the Collection interface')

Awakening consists of a change in awareness, of one's total relation to one's self and the world.

"Is greater than or equal to" is an example of a total relation (this definition for total is different from left total in the previous section).

This functor has a left adjoint (sending every set to that set equipped with the equality relation) and a right adjoint (sending every set to that set equipped with the total relation).

On the other hand, "is less than" is not a total relation, since one can pick two equal numbers, and then neither the first is less than the second, nor is the second less than the first.

For example, "is less than or equal to" is a total relation over the set of real numbers, because for two numbers either the first is less than or equal to the second, or the second is less than or equal to the first.

This is equivalent to a single and somewhat clearer axiom of fullness: between any two sets a and b, there is a set c which contains a total subrelation of any total relation between a and b that can be encoded as a set of ordered pairs.