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总览 评价 曹俊云 * （ 河南理工大学数信学院，河南焦作 454000； ） 摘要： 无穷是无有穷
曹俊云*
（
河南理工大学数信学院，河南焦作 454000； ）
摘要：
无穷是无有穷尽、无有终了的意思；它不是完成了的实无穷。无尽小数是写不到底的事物；等式2/3=0.666……是虚假的、无用的、无法证明的等式。无尽小数不是实数。实数是现实数量大小的表达符号。每一个正无尽小数都是单调有界递增无穷数列的简写，它是个变数而不是定数。每一个以有理数为项的康托尔基本数列都存在一个唯一的理想实数为其极限，而且等价(也称全能近似相等)的基本数列的极限相同。反之，每一个实数都存在着以它为极限的康托尔基本数列及其惟一的无尽小数表达式。实数的加、减、乘、除运算是它的全能近似值数列（包括它的无尽小数）加、减、乘、除运算的极限。
关键词：
无穷；无尽小数；康托尔基本数列；理想实数；全能近似值数列；全能近似相等
Cao Junyun*
（
school of Mathematics and Intormation engineering Henan Polytechnic University,Jiaozuo 454000； ）
Abstract：
The meaning of infinity is without end; It is not a thing of finished actual infinity. Infinite decimal is a thing of could not be end to write; Equality 2/3=0.666…… is one false, useless and undemonstrable equality. Infinite decimal is not real number. Real numbers are all symbol to express size of actual quantity. Every right infinite decimal is all a simple expression of monotone increasingly and bounded above infinite sequence; it is a variable and is not a constant. Every Cantor's elementary sequence possesses all an ideal real number, which is limit of Cantor's elementary sequence; and those limits of mutual equivalent sequences are same one. On the contrary, every real number possesses all many mutual equivalent Cantor's elementary sequence and one infinite decimal which limits are the ideal real number. The calculation of addition and subtraction, multiplication, division of real number is the addition and subtraction, multiplication, division calculation limit of its omnipotent series of approximation numerical value (contain its infinite decimal)
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