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文[1]介绍了用“子不等式法”证明与自然数n有关的不等式的方法.针对文[1]的遗留问题,文[2]介绍了“子不等式从何而来?”文[2]认为:“一旦证明了子不等式,就……改为非数学归纳法的证明.”但从所举例题来看,“子不等式”均系由数学归纳法的第二步并通过分析法得出,其实质仍为数学归纳法.若要“改为非数学归纳法的证明”,即用“子不等式法”,直接得出“子不等式”并予以证明方可.但子不等式是否存在?能否直接得出?成为解决问题的关键.笔者研究发现,子不等式完全可直接由欲证之不等式直接得出.下面介绍给读者.
In [1], we introduce a method to prove the inequality associated with the natural number n using the “subinequalities method.” For the legacy problem of [1], the paper [2] introduces “where does the sub-inequality come from?”[2] It is believed that: “Once a sub-inequality is proved, it is replaced with a proof of non-mathematical induction.” However, from the point of view of the example, “sub-inequalities” are all derived from the second step of mathematical induction and are analytically derived. The essence is still the mathematical induction method. If we want to “change to the proof of non-mathematic induction method”, we use the “sub-inequalities method” to directly derive the “sub-inequality” and prove it. But does the sub-inequality exist? Whether it is directly drawn or not is the key to solving the problem. The author’s research found that the sub-inequalities can be directly obtained directly from the inequality they want to prove. The following is introduced to the reader.