\begin{definition}[Definition:Ordering of Cuts]
Let $\alpha$ and $\beta$ be cuts.
$\alpha$ and $\beta$ conventionally have the following ordering imposed on them, as follows:
:$\alpha$ '''is less than or equal to''' $\beta$, denoted $\alpha \le \beta$
{{iff}}:
:$\alpha = \beta$ or $\alpha < \beta$
where $<$ denotes the strict ordering relation between $\alpha$ and $\beta$.
This can also be expressed as $\beta \ge \alpha$.
\end{definition}