极限概念的意义与数学发展的语言转向  

Meaning of Limit and Language Change of Mathematical Development

作　　者：谢琳[1] 战玲[1] 

机构地区：[1]辽宁师范大学数学学院

出　　处：《数学教育学报》2010年第5期90-92,共3页Journal of Mathematics Education

基　　金：国家自然科学基金项目——低维流形中若干问题的研究(10771023)

摘　　要：ε-语言极限概念的核心意义在于摆脱了此前所谓“变量数学”关于数学对象的动态描述方式，并明确界定了无限运算的含义．从而使“变量数学”的思维方式和语言表达逐渐被扬弃，理论数学在更高层面上“回归”为对静态形式对象进行构建和逻辑分析的阶段．那些曾在做积分发展过程中引起过逻辑混乱的概念基本被清除掉了．The core significance of the concept about limit, expressed by c--language, consists in breaking away from a dynamical describing method of ＂variable mathematic＂ and defining the meaning of infinite operation clearly. Therefore, the development of mathematics had been changed greatly. The way of thinking and language, which was based on ＂variable mathematics＂ had been abandoned gradually. The theoretical mathematics returned to a stage which static objects can be established and analysis logically. As a result, the concepts, which had caused logical confusion, in the development of calculus, had been completely liquidated.

关 键 词：极限 无穷小 数学结构 逻辑 

分 类 号：G40-20[文化科学—教育学原理]