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arXiv 1202.4153math.HOmath.CAmath.LO
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精神分析学史上的十大误区及其破除

Ten Misconceptions from the History of Analysis and Their Debunking

Piotr Blaszczyk, Mikhail G. Katz, David Sherry

摘要:

关于无穷小被康托、戴德金和维尔斯特拉斯的“伟大的三巨头”“消灭”的普遍观点,被一系列关于无穷小丰富数系统的不间断的工作所驳斥。消除主张是由三巨头追随者创造的一种过于简单化的说法,他们倾向于把分析的历史看作是朝着维尔斯特拉斯的epsilontics的光辉未来的一次预先注定的进军。在本文中,我们记录了分析历史的扭曲,这种扭曲源于本体论最低限度主义的三巨头意识形态,它用一个单一的数字系统来识别连续统。这种时代错误的扭曲的特点接受解释斯蒂文,莱布尼茨,达朗贝尔,柯西,和其他人。

英文摘要:

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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