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

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 .