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证明任何一个数学命题,都应要求论证方法本身合理正确。就是说,论证方法本身不能违背逻辑规则。最近,我们对中学数学课本中出现的所谓“逆证法”作了一些探讨。现提出一些看法,以期引起大家共同研究。为了说清问题,我们把中学数学课本中有关的一段转录如下: “证明不等式也可以用逆证法,就是先假定这个不等式(原命题)成立,逐步推出一个已知的不等式(真命题),如果推理的每一步都可逆,那么就可以断定所给的不等式(原命题)成立。例3 已知a,b,m都是正数,并且 aa/b 证明假定a+m/b+m>a+b成立,两边都乘以正数
To prove any mathematical proposition, the argument method itself should be required to be reasonable and correct. That is to say, the argument method itself cannot violate the logic rules. Recently, we have discussed some of the so-called “antitrust methods” that appear in middle school math textbooks. Some views are now proposed in order to arouse everyone’s joint research. In order to clarify the issue, we transcribe the relevant paragraph in the middle school mathematics textbook as follows: “The proof inequality can also be used to reverse the law, that is, first assume that the inequality (original proposition) is established, and gradually introduce a known inequality (true proposition), If every step of inference is invertible, then it can be concluded that the given inequality (original proposition) is true.Example 3 Given that a, b, m are all positive numbers, and aa The /b proof assumes that a+m/b+m>a+b holds, and both sides are multiplied by a positive number