无穷小的

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

定理 2 有界函数与无穷小的乘积是无穷小。

The product rule and chain rule, the notion of higher derivatives, Taylor series, and analytical were introduced by Isaac Newton in an idiosyncratic notation which he used to solve problems of mathematical physics .

该产品的规则和链的规则，概念，更高的衍生物，泰勒级数，并分析介绍了牛顿的特殊符号，他用来解决问题的数学物理。在他的出版物，牛顿改写他的想法，以适应数学习语的时间，取代的计算几何无穷小的等价论点被认为是无可指责的。

An immeasurably or incalculably minute amount or quantity.

无穷小的数量非常小，几乎无法测量的数量

This paper tries to give a definition of the sum and the product of infinite infinite simal,and it also tries to give some examples to illustrate the sum and the product of infinite infinite simal being or not being infinite simal.

给出了无限个无穷小的和、积的一种定义，并用例子指出无限个无穷小的和、积既可能是无穷小，也可能不是无穷小。

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。

The contents of the abstract of the short Communication is:"The paper gives a complete differential partition to a Euclidean straight line with a fixed frame, and three axioms for the integral of infinitesimals indexed by real numbers; proves in standard mathematics there are positive infinitesimals outside of real number set; Gives cosmic, macro and micro counterexamples to two axioms in Jordan, Carathéodory, and Lebesgue measure theory; transforms Weierstrass limit into Huang limit, Cantor continuum into Huang continuum, and Newton-Leibniz formula into Huang formula."

这个短的发言的摘要的内容如下："此文对一条确定了固定标架的欧几里德直线给出了完整的微分分拆，并对以实数为标号的无穷小的积分给出了三条公理；在标准数学中证明了在实数集合之外存在正的无穷小；对若当，卡拉特欧多里和勒贝格测度论中的两条公理给出了宇观的，宏观的和微观的反例；将外尔斯特拉斯极限改进为黄氏极限，将康托连续统改进为黄氏连续统，和将牛顿－莱布尼茨公式改进为黄氏公式。"

These ideas were systematized into a true calculus of infinitesimals by Gottfried Wilhelm Leibniz , who was originally accused of plagiarism by Newton.

These想法系统化成为一个真正的结石无穷小的哥特弗里德威廉莱布尼茨，谁最初被控剽窃的牛顿。

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。

Leibniz also freely invoked mathematical entities he called infinitesimals, manipulating them in ways suggesting that they had paradoxical algebraic properties.

莱布尼茨自由运用他称之为&无穷小&的数学单位，并以各种他们相悖的代数性质进行运算。乔治？

The contents of the abstract of the short Communication is:"The paper gives a complete differential partition to a Euclidean straight line with a fixed frame, and three axioms for the integral of infinitesimals indexed by real numbers; proves in standard mathematics there are positive infinitesimals outside of real number set; Gives cosmic, macro and micro counterexamples to two axioms in Jordan, Carathéodory, and Lebesgue measure theory; transforms Weierstrass limit into Huang limit, Cantor continuum into Huang continuum, and Newton-Leibniz formula into Huang formula."

这个短的发言的摘要的内容如下：&此文对一条确定了固定标架的欧几里德直线给出了完整的微分分拆，并对以实数为标号的无穷小的积分给出了三条公理；在标准数学中证明了在实数集合之外存在正的无穷小；对若当，卡拉特欧多里和勒贝格测度论中的两条公理给出了宇观的，宏观的和微观的反例；将外尔斯特拉斯极限改进为黄氏极限，将康托连续统改进为黄氏连续统，和将牛顿－莱布尼茨公式改进为黄氏公式。&

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。