Infinity

Eastern and western series in Qingtimes is comparatively studied and the opinions are that the eastern traditional mathematics,different from westerns,are lack of the characteristic that distinguish from science,so the eastern and the western conception of infinite made different progress.

比较了近代东西方的级数论工作,认为中算与和算没有西算那种区别于科学的特性,所以无穷的概念在东西方的进化方式不同。

Ancient Chinese mathematicians had tried to extend them as for as infinite arithmetic,but the result turned out to be a set of formal operations corresponding to polynomial theory.

中算家试图将它们扩张为无穷的算术 ,从而发展出了一套与多项式理论相应的形式运算 。

This paper,we generalize definition of recurring constant,and discuss the line integrals of a function on non-simply connected region with infinite number of holes.

本文广义地定义了循环常数，并对含有无穷多个“洞”的非单连通域上的曲线积分进行了讨论。

Does the Largest Natural Number Exist?——A new method in infinity theory to eliminate the paradox of transfinite numbers(2)

存在最大的自然数吗?——排除超限数悖论,无穷理论的新方案(2)

Second all the problems and paradoxes related to infinitesimal,infinitely great and infinity concepts in the classical infinite theory are.

从新构建的基础理论学的角度,用全新的基础理论学的方法[1],在两个层面上揭示了经典无穷理论体系(无穷观)中所存在的三个本质性缺陷,得到明确的结论:1。

The Puzzling of Infinitude and Precise Definition of Limit;

“无穷”的困扰与“极限”的精确定义(英文)

The perfectibility of the definition about the infinitude in mathematics was analyzed firstly in this paper.

本文首先分析了无穷的数学定义存在的问题,给出了中国传统哲学之物极必反的数学表达。

infinitesimal area

无穷小邻域[面积]

Theorem 2 The product of a bounded function and an infinitesimal is an infinitesimal.

推论1常数与无穷小的乘积是无穷小。

Corollary 1 The product of a constant and an infinitesimal is an infinitesimal.

推论2有限个无穷小的乘积是无穷小。

Theorem 1 The sum of finite number of infinitesimal is an infinitesimal.

定理1有限个无穷小的和也是无穷小。

Notes On Infinity And Infintesimal;

关于无穷小与无穷大关系的一点注记

infinite branch

无穷分枝, 无限分枝

The cars zipped by endlessly.

无穷无尽的车呼啸而过。

Along the margin of a bay:

延伸成无穷无尽的一行；

I have unlimited potential.

我的潜力无穷无尽，

infinite interval

无穷区间, 无限区间

Every comfort is availaBle for ultimate enjoyment.

舒适无比，享乐无穷

The Derivate of the Function with Finite Limit at the Infinite Point;

在无穷远处有有穷极限的函数的导数

Zero reactance;Infinite reactance;Zero reactance - Infinite susceptance;Infinite reactance - Zero susceptance

零阻抗;无穷大阻抗;零阻抗-无穷大电纳;无穷大阻抗-零电纳

an exuBerant growth of moss;

苔藓无穷尽地大量生长;

an unfailing source of good stories.

好故事的无穷尽源泉

"Beauty is potent, But morality is omnipotent"

美貌固有力,道德力无穷

A fine example has boundless power.

榜样的力量是无穷的。

We usually mean infinitely large.

我们通常是指无穷的大。