On the classic paradox of infinity and a related function

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-02-01 DOI:10.1093/teamat/hrab001

Chanakya Wijeratne;Rina Zazkis

引用次数: 0

Abstract

In this study we consider a classic paradox of infinity and its variations and suggest how the sources of misleading intuition can be analysed using the concept of uniform convergence of functions. We then examine how six mathematics honour students engage with a variation of the paradox. Despite their advanced mathematical training, the participants experienced considerable difficulty in addressing the presented paradoxical situation. Drawing on data from written responses and individual interviews, we describe the students’ approaches in an attempt to reconcile their intuitive perceptions with their mathematical computations.

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关于经典的无穷大悖论及其相关函数

在这项研究中，我们考虑了一个经典的无穷大悖论及其变体，并建议如何使用函数一致收敛的概念来分析误导直觉的来源。然后，我们研究了六名数学荣誉学生是如何参与悖论的变体的。尽管他们接受了高级数学训练，但参与者在解决出现的矛盾情况方面遇到了相当大的困难。根据书面回复和个人访谈的数据，我们描述了学生的方法，试图将他们的直觉与数学计算相协调。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.