函数形式的单调有界原理及其应用  

Monotone bounded principle of functional form and its applications

作　　者：赵霜 赵莉莉 ZHAO Shuang;ZHAO Lili(School of Mathematics and Statistics,Yunnan University,Kunming 650091,china)

机构地区：[1]云南大学数学与统计学院,云南昆明650091

出　　处：《高师理科学刊》2023年第11期10-13,共4页Journal of Science of Teachers＇College and University

基　　金：云南省教育厅2020年自然科学基金项目(2020J0020)。

摘　　要：单调有界原理是判断极限是否存在的重要准则之一,但大多数教材中仅介绍过数列形式的单调有界原理.为了更好地阐述单调有界原理的本质,将单调有界原理推广到函数的形式,利用函数极限、上确界、下确界的定义进行了证明.给出了相应的函数形式单调有界原理的应用实例.The monotone bounded principle is one of the important criteria for judging the existence of limits,but most textbooks only introduce the monotone bounded principle in the form of series.In order to better explain the nature of monotone bounded principle,the monotone bounded principle is extended to the form of functions,the proof is given by using of the definition of function limit,supremum and infimumthe.Finally,the corresponding application examples of the monotone bounded principle of function form are given.

关 键 词：函数极限 单调有界原理 上确界 下确界 

分 类 号：O175.1[理学—数学]