实数理论

在GO-空间中，不仅给一般拓扑学提供了精彩丰富的例证，而且架设了一般拓扑学和相关数学分支的桥梁，如格论、Domain理论、图论及实数理论等等。

Not only does GO-space provide rich examples , but also GO-space buildes a bridge between general topology and related mathematics branches , such as Lattics theory , Domain theory , Graph theory , Real number theory , etc.

Weierstrass聚点定理、Cauchy收敛准则、区间套定理、确界存在定理、单调有界定理和有限复盖定理是实数理论的六个等价命题。

The six equivalent propositions of real number theory are Weierstrass condensation point theorem , Cauchy criterion for convergence , contract consecutive interval theorem , the existence theorem of supremum and infimum , monotone and boundedness theorem , and finite covering theorem .

实数理论是数学分析的重要基础。

The theory of real number is the important base of Mathematic Analysis .

实数理论的问题与足够准分析简介

The Problem of Real Number Set and the Introduction of Sufficient Accurate Analysis

实数理论再议

A Re-discussion on the Theory of Real Numbers

这劳什子大半都是超实数理论，差不多和一具泡了三千年朝天椒酱的埃及木乃伊一样容易消化。

This kind of stuff is heavy on the surreal number theory : about as digestible as an Egyptian mummy soaked in tabasco sauce for three thousand years .

区间套原理不仅在实数理论中是重要的，而且对于许多应用问题也是重要的。

The purpose of this note is to point out : the principle of nested intervals is important not only in the theory of real number but for various applied problems .

第二：给出了新的模糊数的距离的定义，并在新的定义的基础上，仿照实数系理论的体系，给出了相应的定理和结论。

ⅱ: give a new definition to the distance of the fuzzy numbers . We get the relevant theorems and conclusions based on the new definition , imitating the real analysis .

本文发展了Cantor用基本列构造实数域的理论，提出超基本列的新概念；

This paper develops cantor 's theory of making real numbers field with cauchy sequence . It put forwards the new concept of hyper cau - chy sequence .

实数连续性理论在平面几何上的应用

An Application of the Theory of Real Number 's Continuity in Plane Geometry

实数的连续性理论是构筑极限理论的重要基础；

The theories of real continuity lead to the fundamental basis of limit theory .

然而，他的证明需要另外一个假设，那就是关于“实数”注的理论。

However , his proof required the assumption that the theory of ' real numbers " * was satisfactory .

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”。

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 .