Definition:Subtraction of Cuts

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

Let $\beta - \alpha$ denote the operation on $\alpha$ and $\beta$ defined as $\beta + \paren {-\alpha}$.

Then the operator $-$ is known as subtraction, and $\beta - \alpha$ is itself called the difference between $\beta$ and $\alpha$.

Also see

 * Existence of Unique Difference between Cuts, which shows that the operation is well-defined