infinitesimally

简明释义

英[ˌɪnfɪnɪˈtesɪməli]美[ˌɪnfɪnɪˈtesɪməli]

adv. 极小地

英英释义

单词用法

同义词

反义词

例句

1.I shall never forget that the probability of a miracle, though infinitesimally small, is not exactly zero.

我绝不会忽略奇迹的发生机率，不管它多渺茫，总不是零。

2.That may not seem like much, especially given the proton's infinitesimally tiny size.

这也许并不起眼，尤其是考虑到质子极小的尺寸。

3.So the odds that all five members of the Federal Reserve Board of Governors would be Jewish are infinitesimally small.

所以所有5名“联邦储备理事会”成员会全部是犹太人的怪事的几率是极小的。

4.So, the probability that the whole city burns down is infinitesimally small, right?

在这样的假设下,整个城市都被烧掉的概率,是非常非常小的

5.An infinitesimally small fraction of online transactions can result in chargebacks before they begin to threaten the economic model of providing online payments.

只有极少的在线转账能够在开始威胁到提供在线支付的经济模型之前得到退单支付。

6.The sheen of the flash on the window was replicated by bonfire smoke drifting infinitesimally slowly from behind a fence.

映照在窗台的闪光被围篱后那无穷无尽缓缓漂移的营火炊烟所取代。

7.I believe that life is infinitesimally brief in relation to the immensity of eternity.

我认为，与死后那慢长的永生相比，人生是极其短暂的。

8.An infinitesimally small fraction of online transactions can result in chargebacks before they begin to threaten the economic model of providing online payments.

只有极少的在线转账能够在开始威胁到提供在线支付的经济模型之前得到退单支付。

9.The scientist noted that the concentration of the substance was infinitesimally 微不足道地 low in the sample.

科学家指出该物质在样本中的浓度是微不足道地低。

10.The error in our measurements was infinitesimally 微不足道地 small, making our results highly accurate.

我们测量中的误差微不足道地小，使得我们的结果非常准确。

11.The change in speed was infinitesimally 微不足道地 slight, almost unnoticeable to the driver.

速度的变化微不足道地轻微，几乎对司机来说是不可察觉的。

12.In calculus, we often deal with infinitesimally 微不足道的 small quantities to understand limits.

在微积分中，我们常常处理微不足道的小量以理解极限。

13.The difference in temperature between the two rooms was infinitesimally 微不足道地 small.

这两个房间之间的温度差异微不足道地小。

作文

In the realm of mathematics and science, the concept of infinitesimals plays a crucial role in understanding the behavior of functions and the nature of change. The term infinitesimally refers to quantities that are so small that they approach zero but never actually reach it. This idea is not just a theoretical abstraction; it has practical implications in various fields, including physics, engineering, and economics.To illustrate the significance of infinitesimally small quantities, consider the process of calculating the area under a curve. In calculus, we use the concept of limits to find the area by summing up an infinite number of infinitesimally thin rectangles. Each rectangle's width approaches zero, and as we take the limit, we can accurately determine the area. This method highlights how infinitesimally small changes can lead to significant results when aggregated.Moreover, in physics, the idea of infinitesimally small displacements is essential for understanding motion. When analyzing the trajectory of a moving object, physicists often break down the motion into infinitesimally small time intervals. By doing so, they can apply Newton's laws to derive equations of motion that describe how objects behave under various forces. This approach emphasizes that even the tiniest changes in position or velocity can have profound effects on the overall motion of an object.In economics, the concept of infinitesimally small changes is equally important. Economists often analyze how small variations in price can affect supply and demand. For instance, if the price of a product decreases infinitesimally, it may lead to a significant increase in quantity demanded. Understanding these minute changes allows economists to make predictions about market behavior and inform policy decisions.However, the application of infinitesimally small quantities is not without its challenges. One major issue arises from the philosophical debate surrounding the existence of such quantities. Some mathematicians argue that infinitesimally small values cannot exist in the real number system, while others advocate for their use in non-standard analysis. This ongoing discussion highlights the complexity of mathematical concepts and the need for precise definitions.In conclusion, the term infinitesimally encapsulates the idea of quantities that are extremely small yet significant in various disciplines. Whether in mathematics, physics, or economics, understanding infinitesimally small changes enables us to grasp complex phenomena and make accurate predictions. As we continue to explore the intricacies of our world, the importance of infinitesimally small quantities will undoubtedly remain a vital aspect of scientific inquiry and discovery.

在数学和科学领域，infinitesimally（无穷小量）的概念在理解函数的行为和变化的性质方面起着至关重要的作用。这个术语指的是那些如此之小以至于接近零但实际上从未达到零的量。这一思想不仅仅是理论上的抽象；它在物理学、工程学和经济学等多个领域具有实际意义。为了说明infinitesimally小量的重要性，考虑计算曲线下方面积的过程。在微积分中，我们使用极限的概念通过求和无限多个infinitesimally薄的矩形来找到面积。每个矩形的宽度接近零，当我们取极限时，可以准确地确定面积。这种方法强调了infinitesimally小的变化在聚合时可以导致显著结果。此外，在物理学中，infinitesimally小位移的概念对于理解运动至关重要。在分析移动物体的轨迹时，物理学家通常将运动分解为infinitesimally小的时间间隔。通过这样做，他们可以应用牛顿定律推导出描述物体在各种力作用下行为的运动方程。这种方法强调，即使是最微小的位置或速度变化也可能对物体的整体运动产生深远影响。在经济学中，infinitesimally小变化的概念同样重要。经济学家常常分析价格的微小变化如何影响供需。例如，如果某种产品的价格减少infinitesimally，可能会导致需求量显著增加。理解这些微小变化使经济学家能够预测市场行为并为政策决策提供信息。然而，应用infinitesimally小量并非没有挑战。一个主要问题源于围绕这些量存在的哲学辩论。一些数学家认为，infinitesimally小值在实数系统中不存在，而另一些人则主张在非标准分析中使用它们。这场持续的讨论突显了数学概念的复杂性以及对精确定义的需求。总之，术语infinitesimally概括了在各个学科中极小但重要的量的思想。无论是在数学、物理学还是经济学中，理解infinitesimally小的变化使我们能够掌握复杂现象并做出准确预测。随着我们继续探索世界的复杂性，infinitesimally小量的重要性无疑将继续成为科学研究和发现的一个重要方面。