无限的概念与数学基础(点击标题下载全文) 已下载

作者:曹俊云

作者单位:河南理工大学数学系

摘要:实无限不能随便应用;现行实数理论与ZFC公理集合论中都有矛盾.实践中的除不尽、开不尽、测不准的事实必须得到尊重;对于点、直线、平行线、实数、相等、导数、函数等基本数学名词,都应当提出近似、全能近似、理想三类不同的术语.没有误差的数学理论是从实践中的近似情形取误差界趋向于0的极限得到的.实数系统的可接受性依赖于实践.

关键词:无限公理;全能近似实数;全能近似函数;非欧几何;数轴;实数集;对立统一法则;

DOI:10.16186/j.cnki.1673-9787.2005.02.019

分类号:O143

The concept of infinity and the foundations of mathematics

Abstract:We could not use the concept of Actual Infinity randomly; There are contradictions in current theories of real number and ZFC. The facts of not having the end of some division calculating and some evolution calculating and the fact of not having enough accuracy to measure continuous quantity must be respected. For all the terms of point, straight line, parallel line, real number, equality, function, derivative and so on, we must put forward three different terms of ideal, approximate and omnipotent approximation. The mathematics theory without error, is obtained by taking limit of the error bounds tending to 0 in approximation situation in practice. The acceptability of real number system depends on practice.

 
 
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