Definition:Ordering of Cuts/Strict

Definition
Let $\alpha$ and $\beta$ be cuts.

$\alpha$ and $\beta$ conventionally have the following strict ordering imposed on them, as follows:
 * $\alpha$ is less than  $\beta$, denoted $\alpha < \beta$


 * there exists a rational number $p \in \Q$ such that $p \in \alpha$ but $p \notin \beta$.
 * there exists a rational number $p \in \Q$ such that $p \in \alpha$ but $p \notin \beta$.

This can also be expressed as $\beta > \alpha$.