Last Updated
：2025/11/22
total order
Noun
Japanese Meaning
全順序：集合上の順序関係の一種で、任意の二つの要素が互いに比較可能である（つまり、任意のx, yに対してx ≤ yまたはy ≤ xが成立する）という性質を持つ順序関係。
（ plural ）
Quizzes for review
(set theory, order theory) A partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x).
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total order
If the relation ≤ is a total order on S, then for any x, y ∈ S either x ≤ y or y ≤ x.
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If the relation ≤ is a total order on S, then for any x, y ∈ S either x ≤ y or y ≤ x.
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