浅谈数学分析中否定命题的教学

On the Teaching of Negative Proposition in Mathematical Analysis

在数学分析的学习中,应用反证法论证某一对象不满足某一定义是很基本且重要的,这就要求能够准确的用肯定的语气叙述出定义的否定命题。文章主要介绍一个叙述否定命题的定理,并用这一定理叙述数学分析中函数在某一数集上无界、函数在某一数集上不严格递增、函数不以某个正数为周期、函数不是周期函数以及数列发散等几个常用的否定命题。最后对数学分析的否定命题的教学提出建议。

In the study of mathematical analysis,it is very basic and important to use the method of counter evidence to demonstrate that an object does not meet a definition,which requires us to accurately describe the negative proposition of the definition.This paper mainly introduces a theorem describing negative propositions,and uses this theory to describe several commonly used negative propositions in mathematical analysis,such as function unbounded on a certain number set,function not strictly increasing on a certain number set,function not taking a positive number as the period,function not periodic function and sequence divergence.Finally,it puts forward some suggestions on the teaching of negative proposition of mathematical analysis.