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。
all the problems and paradoxes related to infinitesimal、infinitely great and infinity concepts in prese.
用全新的基础理论学的方法,深入揭示、分析了经典无穷理论体系(无穷观)中所存在的三个本质性缺陷,进一步介绍了新构建的无穷理论体系的特点,得到明确的结论:1)人类沿用了几千年的经典无穷理论体系不管从宏观或微观的角度都无法真正从质上与量上描述与认识客观世界中存在的无穷事物;2)现有人类知识大厦中所有与“无穷”、“无穷小”、“无穷大”概念相关的悖论与难题在经典无穷理论体系中是不可解的。
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。
Eastern and western series in Qingtimes is comparatively studied and the opinions are that the eastern traditional mathematics,different from westerns,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。
This paper discusses how to teach students"the product of infinite infinitesimals isn t necessarily infinitesimal" in teaching "advanced mathematics" Or "Mathematical Analysis",and the author provides some new original examples which had not been seen in currently available textbook and riches the teaching content.
文章对"无穷多个无穷小的乘积不一定是无穷小"这一知识点在"高等数学"或"数学分析"的教学中如何讲授给学生进行了一些有益的探讨,并给出了一些在现有教科书及参考书中未曾见过的独创的新例子,从而丰富了教学内容。