[過去ﾛｸﾞ] 現代数学の系譜11 ガロア理論を読む30 [無断転載禁止]©2ch.net (653ﾚｽ)

現代数学の系譜11 ガロア理論を読む30 [無断転載禁止]©2ch.net http://rio2016.5ch.net/test/read.cgi/math/1492606081/

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470: 現代数学の系譜11 ガロア理論を読む [sage] 2017/05/03(水) 10:09:33.41 ID:hJ9NLdiz いや、まあ、だから、素粒子論が正しいとして、その物理学の基礎付けとして、現代数学は不十分 つまりは、現代数学は無限がまだ分かっていない（十分数学的に扱えていない）という結論だね 個人的見解だが（＾＾； http://rio2016.5ch.net/test/read.cgi/math/1492606081/470

479: 現代数学の系譜11 ガロア理論を読む [sage] 2017/05/03(水) 11:05:23.88 ID:hJ9NLdiz >>470 関連 https://en.wikipedia.org/wiki/Finitism (抜粋) Finitism Main idea[edit source] The main idea of finitistic mathematics is not accepting the existence of infinite objects such as infinite sets. While all natural numbers are accepted as existing, the set of all natural numbers is not considered to exist as a mathematical object. Therefore quantification over infinite domains is not considered meaningful. The mathematical theory often associated with finitism is Thoralf Skolem's primitive recursive arithmetic. History[edit source] The introduction of infinite mathematical objects was a development in mathematics that occurred a few centuries ago. The use of infinite objects was a controversial topic among mathematicians. The issue entered a new phase when Georg Cantor, starting in 1874, introduced what is now called naive set theory and used it as a base for his work on transfinite numbers. When paradoxes such as Russell's paradox, Berry's paradox and the Burali-Forti paradox were discovered in Cantor's naive set theory, the issue became a heated topic among mathematicians. http://rio2016.5ch.net/test/read.cgi/math/1492606081/479

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