Last Updated
：2025/12/04
transitive set
Noun
Japanese Meaning
集合論において、ある集合Xが推移的（transitive）であるとは、任意の元xがXに属しているとき、もしxがさらに元を含む集合であれば、その全ての元もXに属していることを意味する。 / すなわち、もしx ∈ Xかつxが空でない場合、xのすべての要素yについてもy ∈ Xとなる集合である。
（ plural ）
Quizzes for review
(set theory) Any set X such that for any x ∈ X, if y ∈ x then y ∈ X; equivalently, such that if x ∈ X and x is not an urelement then x ⊆ X.
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transitive set
A transitive set X contains every element of any of its members, making it useful in foundational set theory proofs.
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A transitive set X contains every element of any of its members, making it useful in foundational set theory proofs.
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