极限定义的新方式及其应用  

A New Way of Defining Limits and Applications

作　　者：郭林 张海彬 GUO Lin;ZHANG Haibin(School of Mathematics,Shandong Technology and Business University,Yantai Shandong 264005,China;School of Statistics,East China Normal University,Shanghai 200241,China)

机构地区：[1]山东工商学院数学学院,山东烟台264005 [2]华东师范大学统计学院,上海200241

出　　处：《大学数学》2019年第2期62-66,共5页College Mathematics

基　　金：高等学校大学数学研究和发展中心资助(CMC20170402)

摘　　要：数学分析中关于极限的定义,其逻辑的复杂性,已经超出了日常生活中语言,导致初学者不易掌握其本质.拓扑学中网收敛的概念给出了极限的一般形式,但需要更多的知识,不适合初学者掌握.参考利用有向集和网收敛,引出"最终成立"的概念,通过"最终成立"来表达各种极限,进而发现各类极限内在是统一的.在证明某些命题时,"最终成立"简单易懂,有其独到之处.The definition of the limit in mathematical analysis has complicated logic which has gone beyond the language in daily life,making it difficult for beginners to master its essence.The concept of network convergence in topology gives the general form of the limit,but it requires more knowledge,so it is not suitable for beginners to learn.This paper draws forth the concept of “final establishment” through referencing the directed sets and network convergence,and expresses various limits via “final establishment”.Then it finds that the various limits are inherently unified.When we prove some propositions,“final establishment” is easy to understand,owning its unique features.

关 键 词：极限 网收敛 最终成立 

分 类 号：O172.1[理学—数学]