Total relation

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:

$\forall a,b\in X,\ aRb\lor bRa$

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