我们知道,数学中常用的推理方式有归纳推理、演泽推理和类比推理。如果归纳推理的前提中一个或几个判断范围的总和与结论中判断的范围完全相同,则这种归纳推理叫做完全归纳法。显然完全归纳法可以作为数学中的严格推理证明方法。前提的情况是有限多种时使用的完全归纳法称为普通归纳法。在现行中学教材中,“圆周角定理”、“弦切角定理”等都是采用普通归纳法加以证明的。 如果一个命题的题设的判断范围不止一种情况(但为有限种),并且每一种情况的推理证明又有所不同的话,那 We know that inference methods commonly used in mathematics include inductive reasoning, inference reasoning, and analogy reasoning. If the sum of one or more judgment ranges in the premise of inductive reasoning is exactly the same as the range of judgments in the conclusion, this inductive reasoning is called full induction. Obviously, the complete induction method can be used as a strict reasoning proof method in mathematics. The condition of the premise is that the full induction used when there are a limited number of cases is called general induction. In current middle school textbooks, the “circular angle theorem” and “chord angle theorem” are all proved by ordinary induction. If the subject of a proposition has more than one (but finite) judgment, and the proof of reasoning in each case is different, then