关于极限八个等价定理的循环证明

A Circulatory Demonstration of the Eight Equivalent Theorems on Limit

使用分析的常用技巧对极限的八个等价定理给出了循环证明,体现了分析方法的技巧性,并且提出了以“基本列必收敛”为公理的公理化体系。

This paper presents a cyclic chain of proofs for the eight equivalent theorems by using the regular techniques in the calculus. The approach shows the technical property of calculus method and, most importantly, provides the reform approach that is based on the axiom ＂fundamental sequence must be convergent＂.