单词 | Dedekind cut |
释义 | Dedekind cut (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 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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