【摘要】反证法是数学思维的一种，在许多较为复杂的数学问题的论证中时颇有价值的。充分运用反证法可以帮助学生迅速解决一些难题。它以其独特的证明方法和思维方式对培养学生逻辑思维能力和创造性思维有着重大的意义。反证法是从反面的角度思考问题的证明方法，这种应用逆向的思维方法，可以使很多难题处理起来简便，因此反证法是一种重要的证明方法。本文主要介绍了反证法，反证法的常用七个场合,以及反证法在代数、数论、几何、组合中的应用.

【关键词】反证法;反设;归谬;结论;矛盾.

Abstract: As a form of mathematical thinking, apagoge acts on considerable value in the demonstration of some complicated mathematical problems. The full use of apagoge can help the students figure out mathematical conundrum quickly. Then the distinct method of proof and mode of thinking of the apagoge have a significant meaning on the education of the students, especially at the aspect of logical thinking ability and productive thinking. On the whole, apagoge is a method of proof, which deliberates problems from the opposite point of view. And due to this application of converse thinking, quite a few of puzzles can be handled simply and conveniently. So the apagoge is a quite important method of proof. The essay mainly introduces the apagoge and its disproof method commonly used seven occasions and reduction to absurdity in algebra , number theory , geometry , combined application .

Key Words: Reduction to absurdity; Counter set; The reduction to absurdity; Conclusion; Contradiction.