费马、莱布尼茨、欧拉及其同伙:极限和阴影概念的真实历史

arXiv: History and Overview Pub Date : 2014-07-01 DOI:10.1090/NOTI1149

Tiziana Bascelli, E. Bottazzi, Frederik S. Herzberg, V. Kanovei, Karin U. Katz, M. Katz, Tahl Nowik, David Sherry, S. Shnider

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引用次数: 41

摘要

费马、莱布尼茨、欧拉和柯西都使用了一种或另一种形式的近似等式，或抛弃“可忽略”项的思想，以获得正确的解析答案。他们的推理动作在现代无限小理论的背景下找到了合适的代理，特别是影子的概念。给出了减少实函数重排的一个应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow

Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.

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arXiv: History and Overview

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