| 用连续归纳法证明实数系中的定理 |
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| 引用本文： | 徐永春,关金玉,李博,梅瑞. 用连续归纳法证明实数系中的定理[J]. 数学的实践与认识, 2007, 37(1): 144-146 |
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| 作者姓名： | 徐永春 关金玉 李博 梅瑞 |
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| 作者单位： | 河北北方学院数学系,河北,张家口,075028 |
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| 摘 要： | 引入实数的连续归纳法,并利用实数连续归纳法证明了实数系中的C auchy收敛准则;给出并证明了实数连续归纳法的另一种形式,利用新形式的连续归纳法证明单调有界定理.
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| 关 键 词： | 连续归纳法 归纳起点 归纳推断 |
| 修稿时间： | 2006-09-24 |
Proving Theorems in Real Number Field by Means of Continual Induction |
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| XU Yong-chun,GUAN Jin-yu,LI Bo,MEI Rui. Proving Theorems in Real Number Field by Means of Continual Induction[J]. Mathematics in Practice and Theory, 2007, 37(1): 144-146 |
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| Authors: | XU Yong-chun GUAN Jin-yu LI Bo MEI Rui |
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| Abstract: | This article is to introduce continual induction and to prove Cauchy Convergence Principle by means of it,then to prove Monotone Convergence Theorem by using a new form of Continual Induction,which is put forward and proven in this article. |
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| Keywords: | continual induction initial point of induction inductive inference |
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