用实数完备性证明闭区间上连续函数的有界性  

On the Proofs of the Boundedness of the Continous Function in the Closed Interval with the Real Number Completeness

作　　者：胡亚红[1] 

机构地区：[1]丽水学院数理学院,浙江丽水323000

出　　处：《丽水学院学报》2010年第5期8-10,共3页Journal of Lishui University

基　　金：丽水学院教改重点资助项目(07JZ10)

摘　　要：用实数完备性定理(区间套定理、确界原理、单调有界定理、柯西收敛准则),直接证明了闭区间上连续函数的有界性,从一侧面反映了实数完备性的6个基本定理是互相等价的。In the present paper,the boundedness of the continous function in the closed interval is proved directly with the theorems of the real number completeness,such as the nested interval theorem,the principle of exact bounds,the principle of monotonicity and boundedness as well as the Cauchy convergent norm.This paper also reveals the equivalence of the six theorems on the real number completeness from one side.

关 键 词：区间套定理 确界原理 单调有界定理 柯西收敛准则 有界性定理 

分 类 号：O172.13[理学—数学]