在中学数学中,某些理論若用直接証明,便会太复杂,使学生不易掌握;另外,有时学生还不具备用来証明理論的一些知識,使理論不能得到应有的邏輯上的承认。在这种情况下,若用反証法来讲解是很有成效的,可以达到讲透教材的目的;可以給学生解答一些比較困难的問題。現在举几个例題說明如下: 例1.当我們讲高中代数第七章內“§94对数的定义”时,教材中写着“……我们可以証明(証明很繁,这里省略不讲),一定有唯一的值x=b能够使 2~b=5. 这里所說的“証明很繁”,指的是直接証明很繁,但是我們如果用反証法可証明如下,中学生接受起来并不觉得困难。 証.假设当x=b及x=b′时,都能使2~x=5成立,即2~b=5,2~(b′)=5。 In middle school mathematics, if certain theories are directly proved, they will be too complex and difficult for students to master. In addition, students sometimes do not have some knowledge to prove the theory, so that the theory cannot get the necessary logical recognition. In this case, if the use of anti-evidence method to explain is very effective, you can achieve the purpose of teaching through the textbook; students can answer some of the more difficult problems. Now a few examples are described as follows: Example 1. When we talk about “the definition of the logarithm of § 94” in the seventh chapter of the high school algebra, the textbook says "... we can prove it (verification is very complicated, and the explanation is omitted here). There must be a unique value of x=b to make 2~b=5. The “prove to be very complicated” here refers to the direct proof that it is very complicated, but if we use the anti-evidence method, we can prove it as follows. Difficulties: Proof. Assume that when x=b and x=b’, 2~x=5 holds, ie, 2~b=5 and 2~(b’)=5.