基于实数连续性定理等价的新探讨  

A New Exploration to the Equivalence Theorems of Real Continuity

作　　者：朱永生[1] 林立军[1] 

机构地区：[1]哈尔滨师范大学呼兰学院数学系,黑龙江呼兰150500

出　　处：《锦州师范学院学报（自然科学版）》2003年第2期55-56,共2页Journal of Jinzhou Normal College (Natural Science Edition)

摘　　要：实数集关于极限的运算是封闭的 ,这就是实数的连续性 ;实数的连续性理论是构筑极限理论的重要基础 ;实数连续性定理虽然数学表现形式不同 ,但它们都描述了实数的连续性 ,它们彼此是等价的 ,即任意一个定理都是其它定理成立的充要条件 ,另辟蹊径对其等价性进行了新的探讨。What is called 'real continuity' ? Namely , limit operations in the collection of real numbers are closed . The theories of real continuity lead to the fundamental basis of limit theory . Though the theorems of real continuity embody different mathematical forms , they are all the varied equivalent characterizations of the real continuity , that is to say , every theorem is the tenable full and essential condition of other theorems , their equivalences can be proved by the means which this article discuss .

关 键 词：实数 连续性定理 极限 有限覆盖定理 确界定理 单调有界数列 闭区间套定理 Cauchy收敛原理 

分 类 号：O171[理学—数学]