超实数

研究了超实数＊R上的两种常用拓扑&Q－拓扑及S－拓扑的结构.证明了（＊R，Q）是完全不连通的；

Two kinds of useful topology , i. e.Q-topology and S-topology on the field of hyperreals are studied . Some basic properties of them are proved : ( R , Q ) is totally disconnected ;

关于超实数域R的基数的一些注记

Notes on cardinal number of the hyperreal number field R

从超实数域R到R内的函数的两种连续性

Two kinds of continuity of functions from hyperreal number field R into R

超实数域R的序型

Order types of hyperreal fields

在超实数域R~上对Abel第一定理的扩充

The extended Abel theorem I over the field of hyper-real numbers

在超实数域上对自治系统全局渐近稳定性的扩充

The expansion of hyper-global asympotic stability of autonomous system in hyper-real number region

超实数域R~的性质

The Property of Hyper - Real Numbers R

在超实数域上对标准分析的级数判别法中不定型的区分

Specification of indefinite form about decicion method of series of standard analysis at field hyper-read numbers

提出一个新观点：超实数具有变与不变的对立统一性；

We put forward a new idea : hyper-real numbers have the unity of opposites between motion and rest .

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 .

从有理数到实数，从实数到超实数，超限数以及联系数，数的概念的每一次扩充，都为数学提供了新的方法和新的理论，从而也开辟了新的研究领域。

From the rational numbers to the real numbers and from the real numbers to the transfinite real numbers , the transfinite cardinal numbers , combined numbers . The conception of the numbers is extended every time . They all provide new methods and new theories .