全能近似分析下的无尽小数理论1

曹俊云¹，曹凯²

（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“无有穷尽”、“无有终了”的；无穷大是无有穷尽的大，是无限变化着的变数，而不是定数。无尽小数是递增的、有界收敛数列的简写；它是随着数列项数变化而变化着的变数，而不是一个定数。无尽小数之间的四则算术运算是收敛数列之间的运算，其运算结果是收敛于实数的收敛数列，这个结果等价于一个无尽小数。

关键词：无尽小数；无穷；无穷大；康托尔基本数列

中图分类号：O143

Theory of Infinite decimal in Omnipotent approximation analysis

Abstract: The meaning of infinite is have not limit and have not end. The meaning of infinity is changed to great have not limit and the infinity is variable of which changing is have not end and it is not constant. The infinite decimal is an abbreviation of infinite sequence which is increasing and bounded and the infinite decimal is a variable which changing followed by number of term in sequence and the infinite decimal is not constant. The four fundamental operations of arithmetic between two infinite decimal is the calculation between two convergent sequences. The result of four fundamental operations of arithmetic between two infinite decimal is a convergent sequence which possessed equivalence relation to an infinite decimal.

Keywords: infinite decimal; infinite; infinity; Cantor’s fundamental sequence





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