数列极限与函数极限的统一

The Unification of the Sequence Limit and Functional Limit

极限思想是高等数学中常用的思想方法,也是解决函数问题最基本和最常用的方法。函数极限表现为自变量在变化过程中函数值的变化趋势;数列作为一种特殊的函数,可以用函数性质及其相关思想方法对数列进行学习和研究;数列极限与函数极限之间存在较多相似之处,但同时也有很多不同之处,研究数列极限与函数极限之间的异同点,就应当把握"数列是特殊的函数"这一关键点。从数列极限与函数极限的定义和性质出发,介绍二者之间的异同点,并从极限的定义、极限的证明、极限的求解方法等方面描述二者之间的统一。

Limit thought is a common thought method in higher mathematics,which is also the most basic and commonly used method in solving function problems and research.The function limit shows the change of function value in the change process of the independent variable.As a special function,the sequence can be learned and studied by the function and its related thought methods.Sequence limit and function limit have many similarities,but also a lot of differences.The study of similarities and differences between the sequence limit and function limit should grasp the ＂ the sequence is a special function＂ as the key point.This article,from the definition and nature of sequence limit and the function limit,introduces the similarities and differences between them,and from the definition of limit,the proof of limit,limit＇s solving method,describes the unification of them.