关于数学分析中适于用反证法证明的问题类型分析

An Analysis of Problem Types Suitable for Proof by Contradiction in Mathematical Analysis

在数学分析中,如果要论证的命题(若A 则B),没有直接证明的正面根据,用反证法证明,此时,只要证明该命题的否定(若A 则不B)与已知条件或者定理、公理等相矛盾即可.而对于论题“若A则B”是否有直接证明的正面根据,如何判断呢?要看数学分析中是否建立了关于B 或不B 的理论.若数学分析中建立了有关B 的理论,则适于用直接证法证明,若建立了关于不B 的理论,则适于用反证法.

In mathematical analysis,if the proposition to be proved(if A then B)has no positive basis for direct proof,it can be proved by contradiction.At this time,it is only necessary to prove that the negation of the proposition(if A then not B)contradicts the known conditions or theorems and axioms.How to judge whether there is a positive basis for direct proof of the topic″If A then B″?It depends on whether the theory of B or not B is established in mathematical analysis.If the theory of B is established in mathematical analysis,it is suitable to prove it by direct proof,and if the theory of not B is established,it is suitable to prove it by contradiction.