用柯西收敛原理证明实数完备性的其它定理

Prove Other Real Number Completeness Theorem Use Cauchy Convergence Principle

遵循学生学习数学分析的知识顺序,从证明柯西收敛原理出发,对实数完备性其它定理进行一一证明,验证与推广了有关学者的论证。

According to the knowledgeorder of mathematical analysis learning and starting from the proof of the Cauchy Convergence Principle, we prove the other theorems on completeness of the set of real numbers, which generalizes some related results given by some other scholars.