\begin{definition}[Definition:Cut (Analysis)/Rational]
Let $r \in \Q$ be a rational number.
Let $\alpha$ be the cut consisting of all rational numbers $p$ such that $p < r$.
Then $\alpha$ is referred to as a '''rational cut'''.
To express the fact that $\alpha$ is a '''rational cut''', the notation $\alpha = r^*$ can be used.
\end{definition}