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2ch■コピペモード□スレを通常表示□オプションモード□このｽﾚｯﾄﾞのURL■項目テキスト700:現代数学の系譜 雑談 古典ガロア理論も読む 19/03/21 15:31:36.36 L2G86nzK.net >>628 関連 https://people.math.ethz.ch/~halorenz/ Lorenz J. Halbeisen https://people.math.ethz.ch/~halorenz/4students/4students.html Some of my lectures https://people.math.ethz.ch/~halorenz/4students/Algebra/AC.pdf G ZARLINO 著 L.J. Halbeisen, Combinatorial Set Theory, Springer Monographs in Mathematics, DOI 10.1007/978-1-4471-2173-2_5, c Springer-Verlag London Limited 2012 (抜粋) P126 NOTES The Axiom of Choice. Fraenkel writes in [26, p. 56 f.] that the Axiom of Choice is probably the most interesting and, in spite of its late appearance, the most discussed axiom of Mathematics, second only to Euclid’s axiom of parallels which was introduced more than two thousand years ago. We would also like to mention a different view to choice functions, namely the view of Peano. In 1890, Peano published a proof in which he was constrained to choose a single element from each set in a certain infinite sequence A1,A2, . . . of infinite subsets of R. In that proof, he remarked carefully (cf. [73, p. 210]): But as one cannot apply infinitely many times an arbitrary rule by which one assigns to a class A an individual of this class, a determinate rule is stated here, by which, under suitable hypotheses, one assigns to each class A an individual of this class. To obtain his rule, he employed least upper bounds. According to Moore [66, p. 76], Peano was the first mathematician who?while accepting infinite collections?categorically rejected the use of infinitely many arbitrary choices. つづく 次ページ最新レス表示レスジャンプ類似スレ一覧スレッドの検索話題のニュースおまかせリストオプションしおりを挟むスレッドに書込スレッドの一覧暇つぶし2ch