查询词典 infinitesimals

Any integer multiple of an infinitesimal is still infinitely small, i.e., infinitesimals do not satisfy the Archimedean property .

这种做法失宠于19世纪，因为这是很难的概念微不足道精确。

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。

Historically, it has been referred to as "the calculus of infinitesimals ", or " infinitesimal calculus ".

结石已广泛应用在科学，经济，工程，是用来解决问题而代数是不够的。

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。

In his publications, Newton rephrased his ideas to suit the mathematical idiom of the time, replacing calculations with infinitesimals by equivalent geometrical arguments which were considered beyond reproach.

他用微积分的方法来解决问题的行星运动，形状，表面旋转流体，在地球的扁率，运动，体重滑动的摆线，并讨论了许多其他问题，他的数学原理。

Infinitesimals out of my life, and many a life

出于我的生命和许多个生命的极微小的东西

In the 19th century, infinitesimals were replaced by limits .

在19世纪，无穷小，取而代之的限制。

Reaching infinitesimals , mathematics, the most exact of the sciences, leaves the process of analysis and enters on a new process of approximating to summing up the unknown infinitesimals .

数学这门最精密的科学获得无限小数的时候，便放弃解析的过程，开始总和未知的无限小数的新过程。

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。&

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。