Trichotomy Law


 * Trichotomy Law (Ordering): An ordering $\preceq$ is a total ordering iff:
 * $\forall a, b \in S: a \prec b \lor a = b \lor a \succ b$


 * Trichotomy Law (Integral Domain): in an ordered integral domain, the positivity property $P$ is such that:
 * $\forall a \in D: P \left({a}\right) \lor P \left({-a}\right) \lor a = 0_D$


 * Trichotomy Law for Real Numbers: $\forall a, b \in \R$, exactly one of the following holds:
 * $(1): \quad a > b$ ($a$ is greater than $b$)
 * $(2): \quad a = b$ ($a$ is equal to $b$)
 * $(3): \quad a < b$ ($a$ is less than $b$).