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Let $S$ be a set.
- $a \mathrel \RR b$
- $a = b$
- $b \mathrel \RR a$
A classic example of a trichotomy is the standard less than ordering on the set of real numbers.
- Trichotomy Law: an ordering $\prec$ is a strict total ordering if and only if $\prec$ is a trichotomy.
- Results about trichotomies can be found here.