分类讨论是一种重要的数学思想方法,当问题的对象不能进行统一研究时,就需要对研究的对象按某个标准进行分类,然后对每一类分别研究,给出每一类的结论,最终综合各类结果得到整个问题的解答.实质上分类讨论就是“化整为零,各个击破,再集零为整”的数学策略.分类原则:(1)所讨论的全域要确定,分类要“既不重复,也不遗漏”;(2)在同一次讨论中只能按所确定的一个标准进行;(3)对多级讨论,应逐级 Classification discussion is an important method of thinking in mathematics. When the object of the problem cannot be studied in a unified way, it is necessary to classify the objects of the study according to a certain standard, and then study each class separately and give conclusions for each class. The final synthesis of various results is the answer to the whole question. Essentially, the classification discussion is a mathematical strategy of “dividing into zeros, breaking each, and then reorganizing zero into whole”. Classification principles: (1) The whole field in question must be determined, The classification should be neither repeated nor missed; (2) it can only be conducted in the same discussion in accordance with one of the criteria determined; (3) For multi-level discussion, it should be leveled