Trichotomy

Generally a trichotomy is a splitting into three disjoint parts. In mathematics, the most concrete law of trichotomy that is usually seen is the statement that for any real numbers x and y, exactly one of the following relations holds:

More generally, a law of trichotomy is any statement that for some binary relation on some set S, which we may denote by using the "less than" symbol "<", and for any two members x, y ∈ S, exactly one of the relations above holds. This is exactly equivalent to saying that the binary relation in question is a linear ordering of the set S.