Dedekind cut

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(mathematics) Any partition of the set of rational numbers into non-empty sets A and B such that all elements of A are less than all elements of B and A contains no greatest element; intended as a construction of a real number.

日本語の意味

有理数全体を、非空な集合 A と B に分割し、A のすべての要素が B のすべての要素より小さいようにし、かつ A に最大の要素が存在しないという条件を満たす分割。実数を構成するための数学的手法の一つ。

英語の意味

(mathematics) Any partition of the set of rational numbers into non-empty sets A and B such that all elements of A are less than all elements of B and A contains no greatest element; intended as a construction of a real number.

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To rigorously construct the real numbers, a Dedekind cut partitions the rational numbers so that one side has no greatest element, thereby representing irrational numbers as gaps.

実数を厳密に構成するために、有理数を二つの非空な集合AとBに分け、Aのすべての元がBのすべての元より小さく、かつAに最大元が存在しないようなデーデキントの切断は、有理数の間の隙間として無理数を表現する。

詳細

意味（1）

(mathematics) Any partition of the set of rational numbers into non-empty sets A and B such that all elements of A are less than all elements of B and A contains no greatest element; intended as a construction of a real number.

More than one formal solution was offered; the one which is easiest to work with (all of the solutions are provably equivalent) is the method of Dedekind cuts.

詳細

Dedekind cuts （ plural ）