infinitesimal

简明释义

英[ˌɪnfɪnɪˈtesɪm(ə)l]美[ˌɪnfɪnɪˈtesɪml]

adj. 无穷小的；无限小的；极小的

n. 无限小；极微量；极小量

复 数 i n f i n i t e s i m a l s

比 较 级 m o r e i n f i n i t e s i m a l

最 高 级 m o s t i n f i n i t e s i m a l

英英释义

单词用法

同义词

反义词

例句

1.They could refuse to light up for no apparent reason, because of some infinitesimal rupture in the filament.

由于灯丝里极其微小的破裂，它们可以没有明显理由地拒绝点亮。

2.And roam it does, from the infinitesimal to the infinite, from the subatomic realm to the far reaches of the universe.

他的智力确实在漫游：从无穷小到无穷大，从亚原子王国到宇宙宽广的领域。

3.An infinitesimal amount, to look at the derivative. Once I do this, how many molecules are in this higher level now?

一个无限小的量，看看能得到什么，一旦我这样做，现在有多少分子能到达这个较高的能级？

4.You are infinitesimal in the crowd, great in the pigsty!

你在人群中渺小，在猪圈伟大！

5.Because the chances of surviving a first category crash landing are so infinitesimal, they're practically nonexistent!

因为在第一类迫降[1]中幸存的几率是极其微小的，实际上就是不可能的。

6.A proton is an infinitesimal part of an atom, which is itself of course an insubstantial thing.

一个质子是一个原子很小的一部分，它自己当然不是一个实在的东西。

7.She spoke with that gentle infinitesimal inflexion of mockery which descended to her from her mother.

她说话时，带着她母亲传给她的那种温柔细致的嘲笑语调。

8.The difference in temperature between the two locations was so small that it could be considered infinitesimal.

这两个地点之间的温度差异微乎其微，可以认为是无穷小。

9.In calculus, we often deal with infinitesimal changes to find the slope of a curve.

在微积分中，我们经常处理无穷小的变化来找到曲线的斜率。

10.The scientist measured an infinitesimal amount of substance in the experiment.

科学家在实验中测量了无穷小的物质量。

11.Even the infinitesimal errors in calculations can lead to significant differences in the final result.

即使是计算中的无穷小误差也可能导致最终结果的显著差异。

12.The infinitesimal changes in pressure were crucial for the experiment's success.

压力的无穷小变化对实验的成功至关重要。

作文

In the realm of mathematics and physics, the term infinitesimal refers to quantities that are exceedingly small, approaching zero but never actually reaching it. This concept plays a crucial role in calculus, where it is used to describe the behavior of functions as they change incrementally. The idea of infinitesimal values allows mathematicians and scientists to perform calculations that involve limits, derivatives, and integrals, which are fundamental to understanding motion, growth, and decay in various contexts. To illustrate the significance of infinitesimal quantities, consider the example of a curve on a graph. When we want to find the slope of the curve at a specific point, we can use the concept of a derivative. The derivative essentially measures how much the function changes as we make an infinitesimal change in the input value. By examining these infinitesimal changes, we can determine the rate of change of the function at that particular point. This process is vital in fields such as physics, where understanding rates of change can lead to insights about velocity, acceleration, and other dynamic phenomena. Furthermore, the application of infinitesimal concepts extends beyond pure mathematics into various scientific disciplines. For instance, in biology, researchers often study populations and their growth rates. When modeling population growth, scientists may use differential equations that incorporate infinitesimal changes in population size over time. By analyzing these infinitesimal changes, they can predict future population dynamics and understand the factors that influence growth or decline. In economics, infinitesimal analysis is also prevalent. Economists frequently examine how small changes in price can affect demand and supply in the market. By utilizing infinitesimal calculus, they can derive demand curves and supply curves, leading to a deeper comprehension of market equilibrium and consumer behavior. This analytical approach enables economists to make informed predictions about market trends and inform policy decisions. Despite its abstract nature, the concept of infinitesimal has profound implications in real-world applications. It encourages us to think critically about change and the limits of our understanding. In a world that often deals with finite quantities, embracing the notion of infinitesimal allows for a more nuanced perspective on the complexities of life. Moreover, the philosophical implications of infinitesimal quantities invite us to reflect on the nature of existence itself. If we consider the universe at its most fundamental level, we encounter particles and forces that operate on scales that can be described as infinitesimal. This prompts questions about the fabric of reality and how we perceive and measure the world around us. The interplay between the infinitesimal and the finite challenges our conventional notions of size, space, and time. In conclusion, the term infinitesimal encapsulates a vital concept in mathematics and science that allows us to explore the subtleties of change and growth. Whether in calculus, biology, economics, or philosophy, the idea of infinitesimal provides a framework for understanding complex systems and phenomena. As we continue to delve into the intricacies of our universe, the significance of infinitesimal quantities will undoubtedly remain a cornerstone of inquiry and exploration.

在数学和物理的领域中，术语infinitesimal指的是极其微小的量，接近于零但从未真正达到零。这个概念在微积分中发挥着至关重要的作用，用于描述函数随着增量变化的行为。infinitesimal值的概念使得数学家和科学家能够进行涉及极限、导数和积分的计算，这些都是理解运动、增长和衰退的基础。 为了说明infinitesimal量的重要性，考虑图表上的曲线示例。当我们想要找到曲线在特定点的斜率时，可以使用导数的概念。导数本质上测量了当我们对输入值进行infinitesimal变化时，函数的变化程度。通过检查这些infinitesimal变化，我们可以确定该函数在特定点的变化速率。这一过程在物理学等领域至关重要，因为理解变化率可以为运动、加速度和其他动态现象提供洞察。 此外，infinitesimal概念的应用不仅限于纯数学，还扩展到各种科学学科。例如，在生物学中，研究人员经常研究种群及其增长率。在建模种群增长时，科学家可能会使用包含随时间变化的infinitesimal变化的微分方程。通过分析这些infinitesimal变化，他们可以预测未来的种群动态，并理解影响增长或下降的因素。 在经济学中，infinitesimal分析也很普遍。经济学家经常考察价格的小变化如何影响市场中的供需关系。通过利用infinitesimal微积分，他们可以推导出需求曲线和供给曲线，从而更深入地理解市场均衡和消费者行为。这种分析方法使经济学家能够对市场趋势做出明智的预测并提供政策决策依据。 尽管其抽象性质，infinitesimal的概念在现实应用中具有深远的影响。它鼓励我们批判性地思考变化及我们理解的界限。在一个通常处理有限量的世界中，接受infinitesimal的概念使我们能够对生活的复杂性有更细致的视角。 此外，infinitesimal量的哲学意义促使我们反思存在本身的性质。如果我们考虑宇宙在其最基本的层面上，我们会遇到在可以被描述为infinitesimal的尺度上运作的粒子和力量。这引发了关于现实结构以及我们如何感知和测量周围世界的问题。infinitesimal和有限之间的相互作用挑战了我们对大小、空间和时间的传统观念。 总之，术语infinitesimal概括了数学和科学中的一个重要概念，使我们能够探索变化和增长的细微差别。无论是在微积分、生物学、经济学还是哲学中，infinitesimal的概念都提供了理解复杂系统和现象的框架。随着我们继续深入探讨宇宙的复杂性，infinitesimal量的重要性无疑将继续成为探索和研究的基石。