巴斯卡拉的除零运算及其在微分学基础上的应用

Q4 Mathematics

Journal of the Indian Mathematical Society Pub Date : 2017-07-01 DOI:10.18311/JIMS/2017/15455

Okoh Ufuoma

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引用次数: 3

摘要

本文主要研究巴斯卡拉的除零运算。这是所有教学分析中最简单的，也是最一致和哲学的。一些数学家试图对此提出质疑，但当我研究他们的推理时，我发现他们这样做是因为他们未能理解零的真实行为。在这篇文章中，我的目的是澄清和证明巴斯卡拉关于涉及零的逼近运算的定律，并暗示除以零的算术运算的基础，即无穷小和极限的方法。

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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Bhaskara's Arithmetic Operation of Division by Zero with Application in the Foundation of the Differential Calculus

This article is concerned mainly with Bhaskara's arithmetic operation of division by zero. This is the simplest of all for teaching analysis and is the most consistent and philosophical. Some mathematicians have attempted to impugn it, but when I examined their reasonings, I observed that they have done so because they have failed to comprehend the true behavior of zero. In this article I have aimed to clarify and justify Bhaskara's law of impending operations involving zero and furnish hints at the foundations upon which the arithmetic operation of division by zero rests its claims to be preferred to its fashionable rivals, the methods of infinitesimals and limits.

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来源期刊

Journal of the Indian Mathematical Society Mathematics-Mathematics (all)

CiteScore

0.50

自引率

0.00%

发文量

期刊介绍： The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.