| 关于Cantor-Hilbert对角线论证方法的分析与研究 |
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| 引用本文： | 黄秀琴,陈桂正,朱梧槚.关于Cantor-Hilbert对角线论证方法的分析与研究[J].南京晓庄学院学报,2010,26(3):20-26. |
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| 作者姓名： | 黄秀琴 陈桂正 朱梧槚 |
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| 作者单位： | 1. 南京晓庄学院行知学院,江苏,南京,211171
2. 南京航空航天大学信息科学与技术学院,江苏,南京,210016 |
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| 摘 要： | 在近现代数学中,通常认为Cantor-Hilbert对角线论证方法是有效的.特别有如文献1]之2.4,列举多条理由论证Cantor-Hilbert对角线论证方法是无懈可击的,但经分析研究文献1]之2.4中所列之论据,其中每一条论据都是没有根据的.文献2]之6.6指出：在兼容两种无穷观之分析方法前提下,可以证明Cantor-Hilbert对角线论证方法并不是无懈可击的.文献3]又在逻辑演算之谓词与集合的层面上,给出了一个不同于文献2]之6.6中的证明方法.因此该文既是一篇评论性文章,其实更是一篇研究性论文.
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| 关 键 词： | 对角线方法 潜无限 实无限 中介公理集合论 近代公理集合论 |
Analysis and Research of Cantor-Hilbert Diagonal Proof Method |
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| HUANG Xiu-qin,CHEN Gui-zheng,ZHU Wu-jia.Analysis and Research of Cantor-Hilbert Diagonal Proof Method[J].Journal of Nanjing Xiaozhuang College,2010,26(3):20-26. |
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| Authors: | HUANG Xiu-qin CHEN Gui-zheng ZHU Wu-jia |
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| Institution: | jia(1.College of Xingzhi,Nanjing Xiaozhuang University,Nanjing 211171,Jiangsu;2.College of Information Science and Technology,Nanjing University of Aeronautics,Nanjing 210016,Jiangsu) |
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| Abstract: | In modern mathematics,the Cantor-Hilbert diagonal proof method is generally considered to be valid.Some articles cited in this paper claim that the Cantor-Hilbert diagonal proof method is unassailable;the authors of the present paper,however,taking into account two infinite views,intend to prove that Cantor-Hilbert diagonal proof method is not invulnerable.This paper is a commentary one,and in fact,it is also a research one. |
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| Keywords: | diagonal method potential infinity actual infinity medium axiomatic set theory modern axiomatic set theory |
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