摘要
从逻辑、无穷观、极限论和证明的思路及具体的操作过程,分析了新发现的康托在实数集合不可数证明中所存在的四种错误,得到"由于与现有经典无穷理论体系、经典极限论和经典数量体系密切相关的数学基础理论中所存在的缺陷,康托在这类证明中无法回避这四种很严重但却很隐蔽的错误"的明确结论.特别是其中的逻辑错误使这样的证明无意中成了一种典型的数学魔术.
Four concealed mistakes in Cantor＇s proofs on the uncountability of real number set are discovered and analyzed from the aspects of logic,infinite theory,limit theory as well as the ideas and operations of the proofs.A conclusion is drown： because of the defects in the foundation of mathematics which is closely related to the present classical infinite theory,limit theory and the classical number system,Cantor unavoidably made four serious but concealed mistakes in his proofs.Particularly,his logical mistake accidentally turned the proofs into a kind of typical mathematical magic.
出处
《喀什师范学院学报》
2011年第6期17-21,共5页
Journal of Kashgar Teachers College
关键词
数学基础
实数集合不可数性
无穷理论体系
逻辑
对角线法
极限论
反证法
The foundation of mathematics
The uncountability of real number set
Infinite theory system
Logic
Diagonal method
Limit theory
Reduction to absurdity
