現代数学の系譜工学物理雑談古典ガロア理論も読む62

現代数学の系譜工学物理雑談古典ガロア理論も読む62at MATH

現代数学の系譜工学物理雑談古典ガロア理論も読む62 - 暇つぶし2ch178: length; the chain ω, n ? 1, n ? 2, ..., 2, 1 has length n for any n. The Mostowski collapse lemma implies that set membership is a universal among the extensional well-founded relations: for any set-like well-founded relation R on a class X which is extensional, there exists a class C such that (X,R) is isomorphic to (C,∈). Reflexivity A relation R is said to be reflexive if a R a holds for every a in the domain of the relation. Every reflexive relation on a nonempty domain has infinite descending chains, because any constant sequence is a descending chain. For example, in the natural numbers with their usual order >=, we have 1 >= 1 >= 1 >= ・・・. To avoid these trivial descending sequences, when working with a reflexive relation R it is common to use (perhaps implicitly) the alternate relation R′ defined such that a R′ b if and only if a R b and a ≠ b. In the context of the natural numbers, this means that the relation <, which is well-founded, is used instead of the relation =<, which is not. In some texts, the definition of a well-founded relation is changed from the definition above to include this convention. https://ja.wikipedia.org/wiki/%E6%95%B4%E7%A4%8E%E9%96%A2%E4%BF%82 整礎関係（多分、上記の和訳（多分ちょっと古い版）） (引用終り) 以上

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