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在中学数学里,有些问题的解决要涉及到实数的分类。所谓实数的分类,就是把实数集R按照某一法则分成若干个叫做类的子集A_1,A_2,…,A_n,使得R中的每一个元素属于且仅属于一个类,即A_1∩A_2∩…∩A_n=φ,A_1∪A_2∪…∪A_n=R,那末这些类的全体就叫做对实数集R的一个分类。其应用常见子含参数的讨论问题,解题时将参数的允许值范围A(A是实数集R或R的一个子集)按照问题的特性分成若干个类A_1,A_2,…,A_n,然后进行讨论。
In middle school mathematics, the resolution of some problems involves the classification of real numbers. The so-called real number classification is to divide the real number set R into a number of subsets called classes A_1, A_2, ..., A_n according to a certain rule, so that each element in R belongs to and belongs to only one class, namely A_1∩A_2∩... ∩A_n=φ, A_1∪A_2∪...∪A_n=R, then the whole of these classes is called a classification of the set R of real numbers. It uses common sub-parameters to discuss the problem. When solving a problem, the parameter’s allowable value range A (A is a subset of the real number set R or R) is divided into several classes A_1, A_2, ..., A_n according to the characteristics of the problem, and then have a discussion.