totally ordered

既定 英語（イギリス） (en-GB)

形容詞

比較不可

(set theory, order theory) That is equipped with a total order, that is a subset of (the ground set of) a partially ordered set whose partial order is a total order with respect to said subset.

日本語の意味

全順序が備わっている、すなわち、部分順序集合の特定の部分集合において、任意の二つの要素が比較可能（順序付け可能）である完全な順序関係が成立している状態。

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In order theory, a chain is a totally ordered subset of a partially ordered set in which every pair of elements is comparable.

順序理論では、チェーンとは、任意の2つの要素が比較可能である全順序を備えた部分順序集合の部分集合です。

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意味（1）

(set theory, order theory) That is equipped with a total order, that is a subset of (the ground set of) a partially ordered set whose partial order is a total order with respect to said subset.

(A.2.5) THEOREM If A is a totally ordered ring and if I is a proper order ideal, then A/I is a totally ordered ring (with the operations and order given above).

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