| 书目名称 | Proofs of the Cantor-Bernstein Theorem | | 副标题 | A Mathematical Excur | | 编辑 | Arie Hinkis | | 视频video | http://file.papertrans.cn/762/761276/761276.mp4 | | 概述 | A scenic-view excursion through the developmental area of research mathematics around the Cantor-Bernstein Theorem (CBT) and related results stemming from Bernstein‘s Division Theorem (BDT), with emph | | 丛书名称 | Science Networks. Historical Studies | | 图书封面 |  | | 描述 | .This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos’ celebrated book .Proofs and Refutations.. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly anything but superficial, as the present book also offers new theoretical insights into the methodology of the development of mathematics (proof-processing), with implications for | | 出版日期 | Book 2013 | | 关键词 | Cantor-Bernstein theorem; gestalt in mathematics; history of science; metaphor in mathematics; methodolo | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-0224-6 | | isbn_softcover | 978-3-0348-0788-3 | | isbn_ebook | 978-3-0348-0224-6Series ISSN 1421-6329 Series E-ISSN 2296-6080 | | issn_series | 1421-6329 | | copyright | Springer Basel 2013 |
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