\begin{definition}[Definition:Ordered Integral Domain/Trichotomy Law]
Let $\struct {D, +, \times, \le}$ be an ordered integral domain.
Let $P$ be the strict positivity property on $D$
The property:
:$\forall a \in D: \map P a \lor \map P {-a} \lor a = 0_D$
is known as the '''trichotomy law'''.
That is:
:Every element of $D$ is either strictly positive, or strictly negative, or zero.
\end{definition}