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 either a is related to b or b is related to a (but not both).

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. The relation "is a subset of" is also not total.

A common total relation is the total order.