example of law of trichotomy on ¡

From the axiomatic definition of the real numbers, “” is a relation on$ℝ$ which satisfies the law of trichotomy. That is, for all $a,b\in ℝ$,exactly one of the following is true:

• $a=b$

As an axiom, this is sometimes expressed with $b=0$. That is, for all $a\in ℝ$, $a$ is either positive, negative, or zero.