关于多元函数极限的一点注记

A Note on the Limits of Multivariable Functions

在微积分学中,极限是一个非常基础而重要的概念,是研究函数的一个基本工具.但较抽象,尤其多元函数的情形.目前,在有关微积分的教材中,一元函数极限的概念相对标准且统一,但多元情形较乱,甚至自相矛盾.本文试图就此问题进行研究,并以一元函数极限的概念为标准,给出多元情形一个标准定义.

In the teaching of calculus the limit concept is a very important and basis concept. It is also a basic tool of research functions. This concept is fairly abstract, especially more so in the case of multivariable functions. At present, on about calculus textbook the limit concept of one-variable functions is a relatively standard and uniform one, but the definition of the limit of multivariable functionsare chaotic, even self-contradictory. This article attempts to expand research on this issue, and to introduce a standardized definition of the limit of multivariable functions as a basis for the case of one-variable functions.