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讨论具有某种性质的数学对象是否存在,是数学中的一类基本问题,在中学数学中也很常见。近年来国内外的数学竞赛和大学入学试题中这类问题出现得比较多,引起了中学师生对这类问题的兴趣。本文归纳了在中学范围内证明这类问题的几种方法,很不成熟,敬请指正。一、构造法所谓构造法,就是把具有(或不具有)某种性质的数学对象实实在在的构造出来,从而达到证明的目的。例1 设函数f(x)定义在以原点为对称中心的点集Ⅰ上,则f(x)可以表示为一个奇函数与一个偶
Discussing the existence of mathematical objects with certain properties is a basic problem in mathematics, and it is also common in middle school mathematics. In recent years, more and more problems have appeared in the math contests at home and abroad and the university entrance exam questions, which have aroused the interest of middle school teachers and students in these issues. This article summarizes several methods for proving this type of problem within the secondary school. It is immature. Please correct me. First, the construction method The so-called construction method, is to have (or do not have) a certain kind of mathematical objects constructed in real, so as to achieve the purpose of the proof. Example 1 Let function f(x) be defined on point set I whose center of origin is symmetry, then f(x) can be expressed as an odd function and a couple.