Last Updated：2025/11/26

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(order theory) Of a subset of a partially ordered set; containing elements at least as late as any given element of the set, relative to the given partial order.

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cofinal

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Source Word

cofinal

Adjective

not-comparable

(order theory) Of a subset of a partially ordered set; containing elements at least as late as any given element of the set, relative to the given partial order.

Japanese Meaning

順序集合（部分順序集合）において、任意の要素に対して、その要素と同等またはそれ以降の位置にある要素を必ず含む部分集合の性質を指す。 / 順序理論における概念で、与えられた部分順序集合の中で、任意の要素よりも遅い（または同位の）要素を含むことを保証する状態を示す。

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In the poset of natural numbers, the set {n ∈ N | n ≥ 100} is cofinal because every natural number is less than or equal to some element of that set.

Google Translation / DeepL Translation

自然数の部分順序集合において、集合 {n ∈ N | n ≥ 100} は、任意の自然数 m に対して m ≤ n を満たす n（かつ n ≥ 100）が集合内に存在するので、順序集合の任意の元より大きいか等しい元を含む部分集合である。

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Sense（1）

(order theory) Of a subset of a partially ordered set; containing elements at least as late as any given element of the set, relative to the given partial order.

The Archimedean property of real numbers means that the natural numbers form a cofinal subset of ℝ.

Google Translation / DeepL Translation

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cofinal

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