从海涅原理看数学分析中连续与离散的辩证关系摘 要：本文主要运用文献研究法、例题分析法、矛盾分析法等方法，首先从海涅定理及其推广形式出发，给出了数学分析中变量的连续与离散的概念，阐述了数学分析中连续与离散的辩证关系是：离散是连续的形成背景，连续是离散的积累结果，连续与离散在一定条件下可以互相转化.其次，在阅读文献的基础上，归纳了连续与离散的两个重要原理，然后论述了正确处理数学分析解题过程中连续与离散的辩证关系的主要思想及方法.再次，基于正确处理数学分析解题过程中连续与离散的辩证关系的指导思想与方法，结合大量具体的实例深刻探讨了连续与离散的辩证关系在解题过程中的实践运用，其中关于连续与离散的辩证关系和运用矛盾分析法分析讨论连续与离散的辩证关系在解题过程中的实践运用是本文的创新点.最后，针对本文进行了系统地总结，并在发现一些不足之处后对下一步的研究作了一定的启示.关键词：海涅定理；连续；离散；辩证关系；辩证否定The Dialectical Relationship Between Continuity and Discreteness in Mathematical Analysis Based on Heine TheoremAbstract:In this paper, we mainly use methods of literature research, sample analysis, contradiction analysis. First of all, from the perspective of Heine theorem and its extended form, this paper presents the concept of continuity and discreteness of variables in mathematical analysis, and expounds the dialectical relationship between continuity and discreteness in mathematical analysis that is: discreteness is the formative background of continuity, continuity is the accumulated result of discreteness, continuity and discreteness can transform each other under certain conditions. Secondly, on the basis of reading literature, this paper summarizes two important principles of continuity and discreteness, and then discusses the guiding ideology and method of correctly handling the dialectical relationship between continuity and discreteness. Thirdly, based on the guiding ideology and method of correctly dealing with the ...
