\begin{definition}[Definition:Negative of Cut]
Let $\alpha$ be a cut.
Let $0^*$ be the rational cut associated with the (rational) number $0$:
:$0^* = \set {r \in \Q: r < 0}$
Let $\beta$ be the unique cut such that:
:$\alpha + \beta = 0^*$
where $+$ denotes the operation of addition of cuts.
Then $\beta$ is referred to as the '''negative''' of $\alpha$.
It is usually denoted $-\alpha$.
\end{definition}