Definition:Subtraction of Cuts
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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
Sources
- 1964: Walter Rudin: Principles of Mathematical Analysis (2nd ed.) ... (previous) ... (next): Chapter $1$: The Real and Complex Number Systems: Dedekind Cuts: $1.20$. Definition