摘要
通过悬而未决的芝诺悖论、贝克莱悖论和罗素悖论这三大悖论家族以及康托在集合论中两个逻辑性错误所暴露的与现有无穷观、数量体系和极限论相关的问题,研究现有极限论中的缺陷与现有无穷观和数量体系中所存在缺陷之间的密切关系,分析了长期被忽视的现有经典极限论在体系性、定性操作和定量操作这三个最基本内容中所存在的问题,揭示了现有经典极限论中的三个主要缺陷.
Connecting with the long existing problems in present classical infinite theory, number system and limit theory exposed by suspending Zeno＇s Paradox, Berkeley＇s Paradox and Russell＇s Paradox as well as Cantor＇s two logical mistakes in set theory, the close relationship between the defects in present infinite theory, number system and the defects in present limit theory are studied. The long neglected defects in the foundation of present classical limit theory of its theoretical system, qualitative operation and quantitative operation are analyzed. Three fatal defects in present classical limit theory are disclosed.
出处
《喀什师范学院学报》
2009年第3期26-31,共6页
Journal of Kashgar Teachers College
关键词
实无穷
潜无穷
泛无穷
忽悠逻辑
贝克莱悖论
极限论
数学哲学
数学基础
Actual infinity
Potential infinity
General infinity
The hoodwinking logic
Berkeley＇s Para-dox
Limit theory
The philosophy of mathematics
The foundation of mathematics
