| "无穷小的比较"的定义及其改进 |
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| 引用本文： | 潘建辉,邓志颖,杨春德."无穷小的比较"的定义及其改进[J].大学数学,2011,27(3):204-208. |
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| 作者姓名： | 潘建辉 邓志颖 杨春德 |
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| 作者单位： | 1. 重庆邮电大学,数理学院,重庆,400065
2. 重庆邮电大学,数理学院,重庆,400065;苏州大学,数学科学学院,苏州,215006 |
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| 基金项目： | 重庆邮电大学自然科学基金项目(A2008-46) |
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| 摘 要： | "无穷小的比较"的现有定义有多种表述形式,但其中不少表述尚不够准确,有失严谨,甚至会导致错误命题的出现.引入"基"概念可使无穷小及无穷小比较的定义更为严谨、简洁、一般化.将无穷小量按含O值点的不同情况分为2类,有利于找出"无穷小的比较"现有定义中存在的问题.通过调整大前提,解决了定义项与被定义项外延不一致的问题;通过转...
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| 关 键 词： | 无穷小量 阶的比较 定义改进 外延 基 |
On the Definitions of Comparison of Infinitesimal And Their Improvements |
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| PAN Jian-hui,DENG Zhi-ying,YANG Chun-de.On the Definitions of Comparison of Infinitesimal And Their Improvements[J].College Mathematics,2011,27(3):204-208. |
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| Authors: | PAN Jian-hui DENG Zhi-ying YANG Chun-de |
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| Institution: | PAN Jian-hui1,DENG Zhi-ying1,2,YANG Chun-de1(1.College of Mathematics and Physics,Chongqing University of Posts and Telecommunications,Chongqing 400065,China,2.School of Mathematical sciences,Suzhou University,Suzhou 215006,China) |
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| Abstract: | There are a lot of definitions about comparison of infinitesimal in current text books,but some of them are not precise or strict enough,and they go so far as to cause incorrect theses.The definitions of infinitesimal and comparison of infinitesimal can be more strict and terse and concise with conception of base.It's favorable for finding out problems from current definitions of comparison of infinitesimal to classify infinitesimals in 2 categories by the situation of their points of zero.The problem that ... |
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| Keywords: | infinitesimal comparison of order definition improvement extension base |
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