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对于与正整数n有关的数学命题,现行教科书(苏教版)仅在《选修2-2》“数学归纳法”一节中有论述,除此再无系统提及.但此类问题,以各种形式散见于包括高考在内的各种考试卷中,不少学生往往找不到合理的解题切入点而束手无策.本文对此类问题的常见解法作些探求,以希指正.一、充分利用正整数的性质现代数学中正整数是通过皮亚诺公理对其进行了刻画和约定的,由此可以推出关于正整数的各种性质.
For mathematical propositions relating to positive integers n, the current textbook (Suprathian version) is discussed only in the section entitled “Elective 2-2” and “Mathematical Induction”, except for the absence of a systematic mention of such problems , In various forms scattered in various exams, including the college entrance examination, many students often can not find a reasonable solution to the entry point and helpless.This paper discusses some common solutions to such problems, to correct me. First, make full use of the nature of the positive integer Modern mathematics is a positive integer through Piano axiom of its characterization and agreement, which can be introduced on the various properties of positive integers.