Total relation

From Exampleproblems

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 (or both).

In mathematical notation, this is

Basically this means that if you are relating members of X (imagine X is a set {a, b, c, ...} ), then for the relation to be total, every memeber must be truthfully related to every other member — i.e. xRy is true or yRx is true or they are both true.

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.cs:Úplná relace