数学分析综合（一） (6-2)

Abstract: On the basis of previous series of papers, cantor diagonal method is put forward and the nested interval method proves that the obvious logic problems in the process of real number are uncountable. Its essence is that the use of reduction to absurdity in this specific case in the past is difficult to detect. Although the uncountability of the set of real numbers is widely accepted, it causes many problems. It makes the so-called mathematical basis extremely complex and full of contradictions. Even more complex and confusing than the other branches of mathematics that are expected to provide a solid foundation, this only suggests that the theory itself has problems. There are two aspects to the practical significance of this paper. One is the mathematical basis and set theory. Second, in the aspect of logic, people should be reminded of the mistakes in the use of proof by contradiction, and that people should adopt a more rigorous and prudent attitude towards any logical, mathematical conclusion and proof. In this paper, we also discuss the problems related to Godel’s theorem and the simplest theoretical problems about the concept of non-limit and infinitesimal of differential method.

文章引用：沈卫国. 数学基础若干问题的创新性思考[J]. 理论数学, 2018, 8(5): 516-533. /10.12677/PM.201...

1. 康托对角线法中的逻辑推理问题详析

根据笔者以往论文中的详尽讨论 [ 1] [ 2] [ 3]，经典的康托对角线法实际隐含逻辑循环或言循环论证，也就是无意中把欲证明的结论当做前提了。用逻辑公式的形式表示，即为：

康托对角线法实际能做到的反证法是：(A→B)→(﹁B→﹁A)

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