分析证明中的反例

The inverse example in the analytic certification

通过高等数学证明问题中的有关例题,说明了在证明某些问题时,必须认真考虑所运用定理的条件和结论。如果考虑不周,往往就得出错误的结果。举出的几个反例,题目本身并不特别复杂,但很有启发性,代表性。除了就本题,结论是正确的,更主要的是让学生养成认真、严谨的思考习惯。分析证明中反例的运用就是对定理条件、结论深刻理解的一个重要的方法。

Through some concerned examples in the certification problems in advanced mathematics,we knew that the conditions and conclusion of the applied theories showld be carefully considered when certifying some problems.If those are not properly considered,wrong results will usually be reached.This thesis gives a few inverse examples.Though the topic itself is not complex,it is enligtening and representative.Apart from the correct conclusion reached,it is more important to help students develop striter way of thinking.The application of inverse examples is an important way to deeply understand the conditions and conclusions of the theory.