# Category:Trichotomies

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This category contains results about Trichotomies.

Let $S$ be a set.

A **trichotomy** on $S$ is a relation $\mathcal R$ on $S$ such that for every pair of elements $a, b \in S$, **exactly** one of the following three conditions applies:

- $a \mathop {\mathcal R} b$
- $a = b$
- $b \mathop {\mathcal R} a$

## Pages in category "Trichotomies"

The following 2 pages are in this category, out of 2 total.