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单词 Dedekind cut
释义

Dedekind cut

A means of constructing the real numbers from the rational numbers, introduced by Richard Dedekind. A Dedekind cut is a subset A of ℚ such that:

(i) ∅ ≠ A ≠ ℚ.
(ii) if x < y are rational numbers and y ∈ A, then x ∈ A.
(iii) if x ∈ A, then there exists y ∈ A such that x < y.

A Dedekind cut A then represents the real number that is its supremum but without having to make reference to real numbers. Order can be defined by A ≤ B if and only if A⊆B and addition by inline

The other arithmetic operations can also be defined but are a little more involved as care must be taken with signs.

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更新时间:2025/5/20 10:24:13