| 引用本文: | 庄陵,唐贤伦,王东,张金荣.实数系完备性基本定理的循环证明(J/M/D/N,J:杂志，M：书，D：论文，N：报纸).期刊名称,2006，（3）： |
| CHEN X. Adap tive slidingmode contr ol for discrete2ti me multi2inputmulti2 out put systems[ J ]. Aut omatica, 2006, 42(6): 4272-435 |
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| 摘要: |
| 在柯西收敛准则的基础上,链式论证了实数系的其他6个基本定理,并最终形成一个完美的论证“环”,体现了数学论证之美;指出了有理数集不具有完备性. |
| 关键词: 实数,完备性,柯西收敛准则,区间套定理,致密性定理,有限覆盖定理,聚点定理 |
| DOI： |
| 分类号:O141.2 |
| 基金项目:重庆邮电学院青年教师科技基金项目,项目编号(A2005-20) |
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| A circulating proof for solving the problem in fundamental theorems of completeness of real number |
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ZHUANG Ling TANG Xian-lun WANG Dong ZHANG Jin-rong
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| Abstract: |
| In this paper,based on the cauchy convergence theorem,catenulation proof of other fundamental theorems of real series is presented,and a circulating proof loop to display the beauty of mathematical proof is formed.The author also points out and validates |
| Key words: real number,completeness,Cauchy Convergence Rule,Interval Sequence Theorem,Bolzano-Weierstrass Theorem,Heine-Borel Theorem,Convergence Point Theorem |
