近来不断有文章对“数学归纳法”这个名称提出异议,有的直截了当:“数学归纳法是一个接一个的假言直言推理的演绎过程。”“数学归纳法是典型的三段论,与归纳推理毫不相干。”有的则说,“一般人们大都承认其主要属于归纳法,但也渗透着演绎思想”,“‘数学归纳法’应该确切地称为‘数学归纳—演绎法’。” 我不同意这些看法,觉得很有必要为“数学归纳法”正正名。 一、演绎与归纳 大家知道,演绎法是由一般结论得出特殊结论的一种推理方法,它的模式是:因为集合A中的每一个元素都具有性质P(大前提),而元素a属于集合A(小 Recently, there have been articles that challenge the name “mathematic induction”, and some are straightforward: “Mathematics induction is the deductive process of hypothetical reasoning one by one.” “Mathematical induction is a typical syllogism, and inductive reasoning It is irrelevant.” Some people say, “In general, people mostly admit that they mainly belong to induction, but they also permeate the idea of ​​deduction.” “The ’mathematical induction method’ should be exactly called ’mathematical induction-deduction method’.” I don’t Agreeing with these views, I feel that it is necessary to justify the ”inductive mathematics method." First, deduction and induction We all know that the deductive method is an inference method that draws special conclusions from general conclusions. Its model is: because each element in the set A has the property P (major premise), and the element a belongs to Collection A (small