Real numbers as infinite decimals

IF 0.3 Q4 MATHEMATICS

Mathematics Enthusiast Pub Date : 2021-01-01 DOI:10.54870/1551-3440.1511

Nicolas Fardin, Liangpan Li

引用次数: 0

Abstract

Stemming from an idea put forward by Loo-Keng Hua in 1962, this article describes an original way to perform arithmetic directly on infinite decimals. This approach leads to a new and elementary construction of the real number system via decimal representation. Based on the least upper bound property, a definition of trigonometric functions is also included, which settles an issue that Godfrey H. Hardy called “a fatal defect” in his Course of Pure Mathematics.

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无穷小数形式的实数

本文根据卢铿华在1962年提出的一个观点，介绍了一种直接对无穷小数进行算术运算的独创方法。这种方法导致了通过十进制表示的实数系统的一种新的基本构造。基于最小上界性质，还包含了三角函数的定义，解决了Godfrey H.Hardy在《纯粹数学教程》中称之为“致命缺陷”的问题。

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

Mathematics Enthusiast MATHEMATICS-

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Mathematics Enthusiast (TME) is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal exists as an independent entity. The electronic version is hosted by the Department of Mathematical Sciences- University of Montana. The journal is NOT affiliated to nor subsidized by any professional organizations but supports PMENA [Psychology of Mathematics Education- North America] through special issues on various research topics. TME strives to promote equity internationally by adopting an open access policy, as well as allowing authors to retain full copyright of their scholarship contingent on the journals’ publication ethics guidelines. Authors do not need to be affiliated with the University of Montana in order to publish in this journal. Journal articles cover a wide spectrum of topics such as mathematics content (including advanced mathematics), educational studies related to mathematics, and reports of innovative pedagogical practices with the hope of stimulating dialogue between pre-service and practicing teachers, university educators and mathematicians. The journal is interested in research based articles as well as historical, philosophical, political, cross-cultural and systems perspectives on mathematics content, its teaching and learning. The journal also includes a monograph series on special topics of interest to the community of readers.