Trichotomy
From Wikipedia, the free encyclopedia.
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.
