\begin{definition}[Definition:Ordering of Cuts/Strict]
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 $\alpha < \beta$
{{iff}}:
:there exists a rational number $p \in \Q$ such that $p \in \alpha$ but $p \notin \beta$.
This can also be expressed as $\beta > \alpha$.
\end{definition}