有序集的一般归纳原理和连续归纳法  

A General Inductive Principle for an Ordered Set and the Continual Induction

作　　者：张景中[1] 冯勇[1] 

机构地区：[1]中国科学院成都计算机应用研究所

出　　处：《科技导报》2008年第6期24-27,共4页Science & Technology Review

基　　金：国家重点基础研究发展计划(973计划)项目(2004CB318003);中国科学院知识创新工程重要方向项目(KJCX2-YW-S02)

摘　　要：证明了一个适用于任意有序集的一般归纳原理,以此为基础导出了数学归纳法、超限归纳法和连续归纳法,从而揭示出三种归纳法的共同基础。文中的例子显示出连续归纳法可用统一模式简单明了地给出数学分析中若干定理的证明,如果在数学专业的分析教学中应用连续归纳法,将有助于克服长期存在的教学难点,提高教学的质量和效率。同时也为分析推理的机械化进行了必要的准备。In this paper, a general inductive principle for any ordered set is proved, and the mathematical induction, the transfinite induction and the continual induction are then deduced. Hence the common basis of them is found. The examples show that the continual induction can be used to prove theorems of mathematical analysis in a simple and clear way. The continual induction, being applied in the teaching of Mathematical Analysis, will help to overcome the long standing teaching difficulties and improve the teaching quality. In the meantime, our result may serve as an essential preparation for mechanization of calculus reasoning.

关 键 词：数学归纳法 连续归纳法 超限归纳法 良序集 

分 类 号：O142[理学—数学]