无穷的概念与实数理论问题—数学基础中的两个基本问题

Questions of Concept on Infinite and Theory of Real Number—Two Fundamental Questions in Mathematical Foundations

摘要: “无穷集合是完成了的事物”的实无穷观点必须取消；无穷的实用意义是“无有穷尽、无有终了的”。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。

Abstract:  The point of view of “infinite aggregate is finished object” on “actual infinity” must be eliminated. 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.