Total relation

From Freepedia

In mathematics, a binary relation R over a set X is total if it holds for all a and b in X that a is related to b or b is related to a.

In mathematical notation, this is

<math>\forall a, b \in X,\ a R b \or b R a.</math>

For example, "is less than or equal to" is a total relation over the set of real numbers, while "is less than" is not.

A common total relation is the total order.