Definition:Equality of Cuts
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Definition
Let $\alpha$ and $\beta$ be cuts such that:
- $p \in \alpha \implies p \in \beta$
- $q \in \beta \implies q \in \alpha$
Then $\alpha$ and $\beta$ are equal.
Sources
- 1964: Walter Rudin: Principles of Mathematical Analysis (2nd ed.) ... (previous) ... (next): Chapter $1$: The Real and Complex Number Systems: Dedekind Cuts: $1.8$. Definition