On History of Epsilontics

arXiv: History and Overview Pub Date : 2016-11-01 DOI:10.14708/AM.V10I0.805

Galina Iwanowna Sinkiewicz

{"title":"On History of Epsilontics","authors":"Galina Iwanowna Sinkiewicz","doi":"10.14708/AM.V10I0.805","DOIUrl":null,"url":null,"abstract":"This is a review of genesis of „e-δ\" language in works of mathematicians of the 19th century. It shows that although the symbols e and δ were initially introduced in 1823 by Cauchy, no functional relationship for δ as a function of e was ever ever specified by Cauchy. It was only in 1861 that the epsilon-delta method manifested itself to the full in Weierstrass de_nition of a limit. The article gives various interpretations of these issues later provided by mathematicians. This article presents the text [ Sinkevich, 2012d ] of the same author which is slightly redone and translated into English. Normal 0 21 false false false PL X-NONE X-NONE /* Style Definitions */ \n table.MsoNormalTable \n {mso-style-name:Standardowy; \n mso-tstyle-rowband-size:0; \n mso-tstyle-colband-size:0; \n mso-style-noshow:yes; \n mso-style-priority:99; \n mso-style-parent:\"\"; \n mso-padding-alt:0cm 5.4pt 0cm 5.4pt; \n mso-para-margin-top:0cm; \n mso-para-margin-right:0cm; \n mso-para-margin-bottom:10.0pt; \n mso-para-margin-left:0cm; \n line-height:115%; \n mso-pagination:widow-orphan; \n font-size:11.0pt; \n font-family:\"Calibri\",\"sans-serif\"; \n mso-ascii-font-family:Calibri; \n mso-ascii-theme-font:minor-latin; \n mso-hansi-font-family:Calibri; \n mso-hansi-theme-font:minor-latin; \n mso-bidi-font-family:\"Times New Roman\"; \n mso-bidi-theme-font:minor-bidi; \n mso-fareast-language:EN-US;}","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: History and Overview","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14708/AM.V10I0.805","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

Abstract

This is a review of genesis of „e-δ" language in works of mathematicians of the 19th century. It shows that although the symbols e and δ were initially introduced in 1823 by Cauchy, no functional relationship for δ as a function of e was ever ever specified by Cauchy. It was only in 1861 that the epsilon-delta method manifested itself to the full in Weierstrass de_nition of a limit. The article gives various interpretations of these issues later provided by mathematicians. This article presents the text [ Sinkevich, 2012d ] of the same author which is slightly redone and translated into English. Normal 0 21 false false false PL X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:Standardowy; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;}

查看原文本刊更多论文

论电磁学的历史

本文回顾了19世纪数学家著作中“e-δ”语言的起源。它表明，虽然符号e和δ最初是由柯西在1823年引入的，但柯西从未规定过δ作为e的函数的函数关系。直到1861年，在魏尔斯特拉斯对极限的定义中，才充分地证明了-方法。这篇文章给出了后来数学家们对这些问题的各种解释。本文采用同一作者的原文[Sinkevich, 2012d]，稍作修改并翻译成英文。正常0 21 false false false PL X-NONE X-NONE /* Style Definitions */ table。MsoNormalTable {mso-style-name: Standardowy;mso-tstyle-rowband-size: 0;mso-tstyle-colband-size: 0;mso-style-noshow:是的;mso-style-priority: 99;mso-style-parent:“”;Mso-padding-alt:0cm 5.4pt;mso-para-margin-top: 0厘米;mso-para-margin-right: 0厘米;mso-para-margin-bottom: 10.0分;mso-para-margin-left: 0厘米;行高:115%;mso-pagination: widow-orphan;字体大小:11.0分;字体类型:“Calibri”、“无衬线”;mso-ascii-font-family: Calibri;mso-ascii-theme-font: minor-latin;mso-hansi-font-family: Calibri;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:宋体;mso-bidi-theme-font: minor-bidi;mso-fareast-language: en - us;}

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

arXiv: History and Overview

自引率

0.00%

发文量