构造法在比大小中的应用探索

An Exploration of the Application of Constructive Methods to Comparing Sizes

构造法是一种重要的比较数与式大小的方法。常见的构造法包括构造图形与构造函数及不等式。用举例的方式分别介绍了常见的几种方法,重点是构造函数法。构造函数法又分利用同构式构建函数、利用等价关系比较大小、利用差商式构建函数、常值换元构造函数、根据凹凸性构造函数、利用不等式特点构建函数等方法。

Construction method is an important method to compare the size of numbers and equations.Common construction methods include constructing graphs and constructing functions and inequalities.Several common methods are introduced with examples,focusing on the constructor method.Constructive function method is divided into the use of isomorphisms to construct functions,the use of equivalence relations to compare the size,the use of difference quotient formula to construct functions and constant value permutation constructive function,according to the concavity and convexity of the constructive function and the use of inequality characteristics to construct functions and other methods.