| 一个关于Peano公理的注记(续) |
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| 引用本文： | 黄崇智. 一个关于Peano公理的注记(续)[J]. 内江师范学院学报, 2007, 22(4): 11-12 |
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| 作者姓名： | 黄崇智 |
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| 作者单位： | 内江师范学院,数学系,四川,内江,641112 |
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| 摘 要： | 证明了关于自然数集={1,2,3,…}的Peano公理系统中的第五条公理(即数学归纳原理)乃该系统中其余公理的逻辑推论.因之,可将它自该系统中删去而仅把它作为一个重要定理以优化该系统.
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| 关 键 词： | 自然数集 Peano公理系统 后继映射 单射 |
| 文章编号： | 1671-1785（2007）04-0011-02 |
| 修稿时间： | 2006-12-14 |
A Note on the Peano''''s Axioms (Continued) |
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| HUANG Chong-zhi. A Note on the Peano''''s Axioms (Continued)[J]. Journal of Neijiang Teachers College, 2007, 22(4): 11-12 |
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| Authors: | HUANG Chong-zhi |
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| Affiliation: | Department of Mathematics, Neijiang Teachers College, Neijiang, Sichuan 641112, China |
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| Abstract: | The writer points out the nonindependence of the Peano's axiom system for the natural numbers.In fact,the writer proves that the 5th axiom in that system,viz,the principle of mathematical induction,is really the logical consequence of the rest in that system. |
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| Keywords: | natural number set Peano's axiom system.successor map injection |
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