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一、引言“函数是什么”,中学生会说:“函数可以用数表、图象或者公式给出.”显然这不是定义.但是,能够避开明确的定义形式并且能够转向描述,函数是怎么给出的,不能说完全不对.数学不能从定义开始.去定义一些概念,我们就不可避免地要在这些定义中应用一些其它的概念.当我们不理解一些概念的含义时,我们就不能向前进一步,不能表述出任何一个定义.因此,任何一个数学理论的叙述要从一些不用定义的基础概念开始.用它们就已经有可能去表述深入一步的任意的概念.
I. INTRODUCTION “What is a function?” The middle school student would say: “Functions can be given by numbers, images, or formulas.” Obviously this is not a definition. However, it is possible to avoid explicit definitions and turn to descriptions. What is the function? Given, can not be completely wrong. Mathematics can not start from the definition. To define some concepts, we will inevitably apply some other concepts in these definitions. When we do not understand the meaning of some concepts, we can not Going further, it is impossible to express any definition. Therefore, any narrative of a mathematical theory should start from some basic concepts that need not be defined. With them, it is already possible to express any concept that goes one step further.