Definition:Apotome/Order

Definition
Let $a, b \in \set {x \in \R_{>0} : x^2 \in \Q}$ be two rationally expressible numbers such that $a > b$.

Let $a - b$ be an apotome.

The order of $a - b$ is the name of its classification into one of the six categories: first, second, third, fourth, fifth or sixth.