博文
无穷的概念与实数理论问题
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曹俊云1，曹凯2
[1] 作者简介：曹俊云（1932-），男，河南唐河人，副教授，从事应用数学与基础数学研究，Email: cjy @ hpu.edu.cn;
曹凯（1985-），男，河南平顶山人，硕士研究生，从事控制理论研究和控制系统设计，Email:caokai.pds@gmail.com
（1. 河南理工大学数信学院，河南焦作，454000;
2. 河南理工大学电气学院，河南焦作，454000;）
摘要：“无穷是现实存在着的”和“无穷是完成了的事物”的观点都必须取消。无穷的实用意义是“无有穷尽、无有终了”。常量性无穷大是不存在的假无穷。自然数集合是一个极限性质的、不能被人构造完毕的理想集合。无尽小数的实用意义是无穷数列的简写。所有理想实数都是康托尔基本数列的极限。理想实数的加、减、乘、除运算是极限性质的运算。
关键词：无穷；无尽小数，自然数集合；理想实数，全能近似实数。
中图分类号：O143
Questions of Concept of Infinite and Theory of real number
Cao Jun Yun1, Cao Kai2
(1. School of Mathematics and Information engineering, Henan Polytechnic University, Jiaozuo, 454000;
2. School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, 454000 )
Abstract: The concept of “infinity is actual existence” and “infinity is finished object” should be eliminated all. The meaning of infinite to use is has not the end. The infinity meant constant is the false infinity which have not exist in real world. The set of natural number is an ideal set which is a limit quality set and could not be end to constitute by mankind. The meaning of infinite decimal to use is the simple writing of infinite sequence. The ideal real numbers are all the limit of Cantor’s fundamental sequence. The calculation of addition, subtraction, multiplication, division is the limit property calculation.
Keywords: Infinite; infinite decimal; set of natural number; ideal real number; Omnipotent approximation real number.https://m.sciencenet.cn/blog-690896-551208.html
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