反证法是高中数学的一种重要的证明方法,在不等式和立体几何的证明中经常用到,在高考题中也经常出现。我们常用的反证法证题的步骤一般可以分为以下三个步骤:(1)做出反设:作出与求证的结论相反的假设;(2)进行归谬:由反设出发,导出矛盾结果;(3)得出结论:证明了反设不能成立,以证明所求证的结论成立。在这个过程中,第二步是关键。而归谬通常包括一下几种途径:与已知条件矛盾,与公理、定理矛盾,与假设矛盾,自相矛盾等。 Proof-of-evidence is an important proof method of high school mathematics. It is often used in the proof of inequality and solid geometry, and often appears in the college entrance examination questions. The commonly used steps of the negative proofs can be divided into the following three steps: (1) making counter-works: making assumptions that are contrary to the conclusions of the proof; (2) (3) concludes: proves that the anti-establishment can not be established to prove the conclusion of the confirmation. In this process, the second step is the key. The return of absurdity usually includes a few ways: contradictory to the known conditions, contradiction with axioms, theorems, contradictions with assumptions and contradictions.