| 关于无穷集合概念的不相容性问题的研究 |
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| 引用本文： | 朱梧槚,肖奚安,杜国平,宫宁生. 关于无穷集合概念的不相容性问题的研究[J]. 南京邮电大学学报(自然科学版), 2006, 26(6): 36-39 |
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| 作者姓名： | 朱梧槚 肖奚安 杜国平 宫宁生 |
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| 作者单位： | 南京航空航天大学,计算机科学研究所,江苏,南京,210016;南京大学,现代逻辑与逻辑应用研究所,江苏,南京,210093;中国人民解放军理工大学,理学院,江苏,南京,210016;南京工业大学,信息科学与工程学院,江苏,南京,210009 |
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| 摘 要： | 文中证明古典集合论与近代公理集合论中的任何一个无穷集合都是自相矛盾的非集。
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| 关 键 词： | 古典集合论 近代公理集合论 可数无穷集合 不可数无穷集合 |
| 文章编号： | 1673-5439（2006）06-0036-04 |
| 收稿时间： | 2006-01-17 |
| 修稿时间： | 2006-01-17 |
The Inconsistency of the Concept of Infinite Sets |
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| ZHU Wu-jia,XIAO Xi-an,DU Guo-ping,GONG Ning-sheng. The Inconsistency of the Concept of Infinite Sets[J]. JJournal of Nanjing University of Posts and Telecommunications, 2006, 26(6): 36-39 |
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| Authors: | ZHU Wu-jia XIAO Xi-an DU Guo-ping GONG Ning-sheng |
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| Affiliation: | 1. Institute of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2. Institute of Modem Logic and its Application, Nanjing University, Nanjing 210093, China; 3. College of Science, PLA University of Science and Technology, Nanjing 210016, China ;4. College of Information Science and Engineering, Nanjing University of Technology, Nanjing 210009, China |
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| Abstract: | In this paper, we prove that there is an inconsistency in any infinite set of the classical set theory or the modem axiomatic set theory. |
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| Keywords: | Classical set theory Modem axiomatic set theory Enumerable infinite set Uncountable infinite set |
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