real number collection

The Real Number Completeness should be highlighted from the completely recognized theory of the real number collection to the explanation of a series of definitions in the Real Number Theory.

从实数集的完备性的公理出发到讲解“实数理论”的一系列定理及用这些定理证明的后继定理都应该突出“实数集的完备性”。

Through a new analysis on the essential relationship between Russell’s Paradox and Cantor’s proof on the uncountability of real number set and the proof on the Cantor’s Theorem of S< P(S) , a mysterious error was found:the very same logic contradiction was applied in both Russell and Cantor’s work.

分析了罗素悖论与康托的实数集合不可数证明及康托定理S

A circulating proof for solving the problem in fundamental theorems of completeness of real number;

实数系完备性基本定理的循环证明

The Provrng of a group of Conclusions on Continuity of real number;

一组实数连续性结论的推证