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- $(1): \quad \alpha \ne \O$ and $\alpha \ne \Q$, that is: $\alpha$ contains at least one rational number but not all rational numbers
- $(2): \quad$ If $p \in \Q$ and $q \in \Q$ such that $q < p$, then $q \in \Q$
- $(3): \quad \alpha$ does not contain a greatest element.
Then $\alpha$ is called a cut.
This category has only the following subcategory.
- ► Dedekind Cuts (1 C, 5 P)
Pages in category "Cuts"
The following 35 pages are in this category, out of 35 total.
- Ordered Field of Rational Cuts is Isomorphic to Rational Numbers
- Ordering of Rational Cuts preserves Ordering of Associated Rational Numbers
- Ordering on Cuts is Compatible with Addition of Cuts
- Ordering on Cuts is Compatible with Addition of Cuts/Corollary
- Ordering on Cuts is Total
- Ordering on Cuts is Transitive
- Ordering on Cuts satisfies Trichotomy Law