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往日(12):数学里“无穷小 infinitesimal”的新符号建议
关键词:无穷小 Keywords: infinitesimal, Infinitely-small function
一、建议用 (躺倒的0)作为“无穷小 infinitesimal”的新符号
以便加深对“无穷小 infinitesimal”和“零 0”之间差异的理解。这是第二次数学危机带来的启示。
微积分里的“无穷小”计算引发的“第二次数学危机”,经历200多年才平息。
二、往日
2009-02-26 我在科学网博客里贴出了《关于无穷小的表示符号 My suggestion of the denotation symbol of infinitesimal》,后来删除了。
重新贴在【科学网论坛 » 管理科学区及其它 » 个人学术展示 » [原创] 关于无穷小的表示符号】。
因为论坛帖出去一段时间(大约1小时?忘了),之后就不能修改了:可以保证“优先权”。而当时的博客,印象是:贴出数年后还可以修改?
下面是BBS的截图:
当初的图片,如下:
三、时光荏苒,光阴似箭,白驹过隙,转瞬即逝
转眼13年多了。
忆往日怆然岁月愁。
叹生命之浪费,独怆然而涕下。
时光荏苒,白驹过隙,其实是忽然而已。
青山依旧在,几度夕阳红?
“天地悠悠,人生匆匆,短短的几十年真如白驹之过隙,转瞬之间就消失了。”“俯仰古今,深感人生短暂,宇宙无限,不觉中流下热泪。”
https://so.gushiwen.cn/mingju/juv.aspx?id=7d1185728d79
"念天地之悠悠,独怆然而涕下!"全诗赏析_古诗文网
参考资料:
[1] Infinity. A.N. Kolmogorov (originator), Encyclopedia of Mathematics.
https://encyclopediaofmath.org/wiki/Infinity
[2] Infinitely-small function. Encyclopedia of Mathematics.
https://encyclopediaofmath.org/wiki/Infinitely-small_function
[3] Infinity, MATHEMATICS,
https://www.britannica.com/science/infinite-set
https://www.britannica.com/science/infinity-mathematics
[4] 胡作玄. 第三次数学危机. 成都:四川人民出版社,1985
[5] Morris Kline. Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press, 1972.
[6] 无穷小 - 百度百科
[7] 澎湃新闻,2022-01-03,无穷小简史:一个数学概念与世界近代历史的发展进程
https://baijiahao.baidu.com/s?id=1720918918522290575&wfr=spider&for=pc
相关链接:
[1] 2012-04-19,增加 SI prefixes 的建议 Suggestion to add the SI prefixes
https://blog.sciencenet.cn/blog-107667-561082.html
[2] 2020-10-05,[严肃内容] 2012-04-13,《增加SI prefixes的建议》,可能属于“0到1”原创
https://blog.sciencenet.cn/blog-107667-1253270.html
[3] 2022-06-23,往日(11)之二:比 Fisher Z Transformation 更好:细节与相关的历史资料
https://blog.sciencenet.cn/blog-107667-1344208.html
[4] 2022-06-21,往日(11):比 Fisher Z Transformation 更好的标准正态分布累积分布erf逼近函数
https://blog.sciencenet.cn/blog-107667-1343914.html
[5] 2022-06-11,往日(10):低阶非线性变换
https://blog.sciencenet.cn/blog-107667-1342532.html
[6] 2022-05-17,往日(9):从忆阻器(Memristor)到电荷源、磁链源
https://blog.sciencenet.cn/blog-107667-1338956.html
[7] 2021-07-15,对2008年《超过指数增长速度的年度用电量曲线拟合预测》一文的一点说明
https://blog.sciencenet.cn/blog-107667-1295579.html
[8] 2021-11-09,[杂录] 对1999年《人类智能模拟的“第2类数学……》一文的一些扼要说明
https://blog.sciencenet.cn/blog-107667-1311664.html
[9] 2022-02-22,往日(8):灵巧床板设想
https://blog.sciencenet.cn/blog-107667-1326509.html
[10] 2021-10-23,往日(7):汉语言改革与文化传承
https://blog.sciencenet.cn/blog-107667-1309140.html
[11] 2021-09-30,往日(6):我们对电力负荷预测的一些看法
http://blog.sciencenet.cn/blog-107667-1306311.html
[12] 2021-05-02,往日(5):1993年 IEEE 的一则 Erratum 勘误(互容 mutual capacitance)
http://blog.sciencenet.cn/blog-107667-1284768.html
[13] 2021-02-03,往日(4):组合预测之谜 forecast combination puzzle
http://blog.sciencenet.cn/blog-107667-1270404.html
[14] 2020-09-13,往日(3):《国家综合能源基地示意图》,2013-01-01,能源发展“十二五”规划
http://blog.sciencenet.cn/blog-107667-1250372.html
[15] 2019-12-04,往日(2):El Nino发生机制的天文成因
http://blog.sciencenet.cn/blog-107667-1208782.html
[16] 2019-02-28,往日(1):小样本数理统计学与“压缩感知 Compressed sensing”
http://blog.sciencenet.cn/blog-107667-1164730.html
感谢您的指教!
感谢您指正以上任何错误!
感谢您提供更多的相关资料!
——— 附录:数学参考资源网址 ———
(1)苏联数学百科全书 Encyclopedia of Mathematics
The Encyclopedia of Mathematics wiki is an open access resource designed specifically for the mathematics community. The original articles are from the online Encyclopaedia of Mathematics, published by Kluwer Academic Publishers in 2002. With more than 8,000 entries, illuminating nearly 50,000 notions in mathematics, the Encyclopaedia of Mathematics was the most up-to-date graduate-level reference work in the field of mathematics.
https://www.encyclopediaofmath.org/index.php/Main_Page
(2)NIST Digital Library of Mathematical Functions
2016-12-21 DLMF Update; Version 1.0.14
http://dlmf.nist.gov/
(3)NIST Handbook of Mathematical Functions Hardback and CD-ROM
Edited by Frank W. J. Olver
University of Maryland and National Institute of Standards and Technology, Maryland
et al.
https://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521192255
http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521192255
(4)Handbook of Mathematical Functions with Formulas,
Graphs, and Mathematical Tables (Partially Mathcad-enabled)
This 1972 book is a compendium of mathematical formulas, tables, and graphs. It contains a very complete table of analytical integrals, differential equations, and numerical series; and includes tables of trigonometric and hyperbolic functions, tables for numerical integration, rules for differentiation and integration, and techniques for point interpolation and function approximation.
https://app.knovel.com/web/toc.v/cid:kpHMFFGMT1/viewerType:toc/root_slug:handbook-mathematical/url_slug:handbook-mathematical/
(5)Alphabetical Index, MacTutor History of Mathematics Archive
https://mathshistory.st-andrews.ac.uk/Biographies/
(5-2)History Topics Index, MacTutor History of Mathematics Archive
https://mathshistory.st-andrews.ac.uk/HistTopics/
The links below will take you to individual articles or to index pages for articles on these topics. School of Mathematics and Statistics , University of St Andrews, Scotland
感谢您提供更多的相关资源!
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