Generally, a trichotomy is a splitting into three disjoint parts.

In mathematics, the law (or axiom) of trichotomy is most commonly the statement that for any (real) numbers x and y, exactly one of the following relations holds:

$x=y,$

$x>y.$

If applied to cardinal numbers, the law of trichotomy is equivalent to the axiom of choice.

In set theory, trichotomy is most commonly defined as a property that a binary relation < has when all its members satisfy exactly one of the relations listed above. Strict inequality is an example of a trichotomous relation in this sense. Trichotomous relations in this sense are irreflexive and antisymmetric.

In taxonomy a trichotomy is speciation of three groups from a common ancestor, where it is unclear or unknown in what chronological order the three groups split. Order theory

In the anthropologic field of theology, and in philosophy, trichotomy is the belief that man consists of three parts; a body, soul, and spirit. This stands in stark contrast to dichotomy.

See also

• Triage

Theology