摘要: 牛顿曾经说过:“反证法是数学家最精当的武器之一”.在现代数学中反证法成为最有用和最有效的解决问题方法之一,反证法是一种简明实用的数学证题方法，也是一种重要的数学思想。反证法独特的逻辑思维方式和证题方法对提高数创造性地分析问题和解决问题的思想素质有重要意义。本文就什么是反证法，反证法的逻辑原理，在使用反证法时要注意事项，以及它与其他证明方法有什么不同这些方面作点初步探讨。

关键字:  反证法；逻辑原理；逆否命题

abstract: Newton once said:" the reduction to absurdity is one of the most useful weapons for mathematician”. the reduction to absurdity is becoming one of the most useful and effective methods in modern mathematics. It is a clear and practical method for proof, what’s more, it’s also an important mathematical thought. It’s unique way of logical thinking and way of doing proof have important meaning for improving the one’s ability of thinking and solving the math problems in a creative way. This thesis pays more attention to the concept of the reduction to absurdity , the logic theory of the reduction to absurdity, some notes of the reduction to absurdity and the uniqueness of the reduction to absurdity.

key words: reduction to absurdity;Logic principle;The negative to deny to set question

目录

一、引言

二、反证法的总体介绍

三、反证法的逻辑原理

1、反证法的逻辑原理证明

2、反证法的五种在实际应用中形式及逻辑等值式

3、反证法逻辑原理小结

四、反证法使用时的注意点

1、宜用反证法的命题

2、如何正确作出假设

3、如何正确导出矛盾

参考文献