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.

Related Topics:
Mathematics - Binary relation - Set

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In mathematical notation, this is

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:orall a, b in X, a R b or b R a.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~