数学分析中几类基本概念及其否定概念的逻辑结构

摘要

学习数学分析，学生首先遇到的困难是基本概念的理解，特别是对两个互为否定概念的关系的理解。产生这些困难的主要原因之一，是对基本概念的逻辑结构没有搞清楚，对两个互为否定概念之间的逻辑关系就更糊涂，往往只知道问题的一面，而不知道问题的另一面，或者只知其然，不知其所以然。因此，进一步揭示数学分析基本概念的逻辑结构，特别是两个互为否定概念的逻辑结构之间的内在关系，对理解和掌握数学分析的基本概念有其重要的意义，也是利用反证法证明有关数学命题的关键。%A learner of mathematic analysis will first meet the obstacle of failing to understand some basic concepts, especially two concepts negating each other. They often fail to grasp the various aspects and only know what they are but fail to know why they are. Therefore, it is of great importance to disclose the logical organizations of basic concepts, especially the inherent relationship of the logical organizations of concepts negating each other in mathematical analysis, and it is also the key to prove some mathematical propositions by contradiction proving.