denumerable

简明释义

英[/dɪˈnjuːmərəbəl/]美[/dɪˈnjuːmərəbəl/]

adj. [数] 可数的；可列的

英英释义

单词用法

同义词

反义词

例句

1.A general model of random walk in time-random environment in any denumerable space is established.

文章在可数状态空间中建立了时间随机环境下随机游动的一个广泛的模型。

2.In this paper, a proof of the theorem on "Any two denumerable Boolean algebras with atoms of the same finite number are isomorphic" is given.

在这篇论文中，定理“任意两个具有相同有限个原子的可数无穷布尔代数是同构的”的一个证明被给出。

3.The permutation of the finite set is introduced into the denumerable set as well as the definition of the basic rotation, the rotation and the composition of the countability.

把有限集中的置换推广到可数集上，引入基轮换、轮换及变换的可数次合成等概念的定义。

4.The permutation of the finite set is introduced into the denumerable set as well as the definition of the basic rotation, the rotation and the composition of the countability.

把有限集中的置换推广到可数集上，引入基轮换、轮换及变换的可数次合成等概念的定义。

5.By using linear operator theory in L2 space, we proved that the operators of this kind has not more than denumerable positive eigenvalues.

运用L2空间上的线性算子理论，我们证明了这类算子存在至多可数个正的本征值。

6.In this paper the properties and fixed point theorems of completely continuous maps on denumerable norm Spaces are studied.

本文讨论可数模空间上全连续算子的有限维逼近定理及该空间的一些性质。

7.The set of natural numbers is denumerable, meaning it can be counted one by one.

自然数的集合是可数的，意味着可以逐一计数。

8.A denumerable set can be put into a one-to-one correspondence with the natural numbers.

可数的集合可以与自然数建立一一对应关系。

9.The concept of denumerable sets is fundamental in set theory.

可数的集合的概念在集合论中是基础性的。

10.In terms of cardinality, any denumerable set has the same size as the set of integers.

在基数方面，任何可数的集合的大小与整数集合相同。

11.The collection of all even numbers is also denumerable.

所有偶数的集合也是可数的。

作文

In the field of mathematics, particularly in set theory, the concept of denumerable sets plays a crucial role in understanding the nature of infinity. A set is termed denumerable if its elements can be put into a one-to-one correspondence with the natural numbers, meaning that we can count them, even if they are infinite. This idea contrasts with non-denumerable sets, which cannot be counted in this manner, such as the set of real numbers. To illustrate the concept of denumerable, consider the set of all integers. We can list them as follows: 0, 1, -1, 2, -2, 3, -3, and so forth. By arranging the integers in this way, it becomes clear that each integer corresponds to a unique natural number. For instance, 0 corresponds to 1, 1 corresponds to 2, -1 corresponds to 3, and so on. Thus, the set of integers is denumerable because we can enumerate them, despite their infinite nature.On the other hand, the set of real numbers between 0 and 1 is an example of a non-denumerable set. Cantor's diagonal argument demonstrates that no matter how we attempt to list all real numbers in that interval, there will always be some numbers left out. This means that the real numbers cannot be matched one-to-one with the natural numbers, making them non-denumerable. Understanding this distinction between denumerable and non-denumerable sets is essential for grasping more advanced concepts in mathematics, such as cardinality and the hierarchy of infinities.The implications of denumerable sets extend beyond pure mathematics. In computer science, for instance, the notion of denumerable sets is significant when discussing algorithms and data structures. Many algorithms operate under the assumption that they can process inputs that are countable, leading to more efficient computations. The ability to categorize data into denumerable sets allows for better organization and retrieval of information, which is vital in our data-driven world.Moreover, the philosophical implications of denumerable versus non-denumerable sets provoke thought about the nature of infinity and the universe itself. If we consider the universe to be denumerable in some aspects, it raises questions about the limits of human understanding and the extent of what can be known. Conversely, recognizing the existence of non-denumerable sets reminds us of the mysteries that lie beyond our comprehension, suggesting that there are infinite possibilities that remain uncharted.In conclusion, the term denumerable is not merely a mathematical abstraction; it serves as a gateway to deeper understanding in various fields. Whether in mathematics, computer science, or philosophy, the concept of denumerable sets challenges us to think critically about the nature of counting, infinity, and the limits of human knowledge. Embracing this concept enriches our perspective and encourages a greater appreciation for the complexities of the world around us.

在数学领域，特别是在集合论中，denumerable 集合的概念在理解无限的本质方面发挥着至关重要的作用。如果一个集合的元素可以与自然数一一对应，即使它们是无限的，我们也可以对其进行计数，那么这个集合就被称为 denumerable。这一观点与非 denumerable 集合形成对比，后者无法以这种方式进行计数，例如实数集合。为了说明 denumerable 的概念，可以考虑所有整数的集合。我们可以将它们列出如下：0、1、-1、2、-2、3、-3，等等。通过这种方式排列整数，可以清楚地看出每个整数都对应于一个独特的自然数。例如，0 对应于 1，1 对应于 2，-1 对应于 3，依此类推。因此，整数集合是 denumerable 的，因为我们可以对其进行枚举，尽管它们是无限的。另一方面，0 到 1 之间的实数集合是非 denumerable 集合的一个例子。康托尔的对角线论证表明，无论我们如何尝试列出该区间内的所有实数，总会有一些数字被遗漏。这意味着实数无法与自然数一一匹配，因此它们是非 denumerable 的。理解 denumerable 和非 denumerable 集合之间的区别，对于掌握更高级的数学概念，如基数和无限等级至关重要。denumerable 集合的影响超越了纯数学。在计算机科学中，例如，denumerable 集合的概念在讨论算法和数据结构时具有重要意义。许多算法假设它们可以处理可计数的输入，从而导致更高效的计算。能够将数据分类为 denumerable 集合，有助于更好地组织和检索信息，这在我们以数据为驱动的世界中至关重要。此外，denumerable 和非 denumerable 集合的哲学意义引发了关于无限和宇宙本质的思考。如果我们考虑宇宙在某些方面是 denumerable 的，这就引发了关于人类理解的局限性和可知事物的范围的问题。相反，认识到非 denumerable 集合的存在提醒我们，还有许多超出我们理解范围的神秘事物，暗示着无限的可能性仍然未被探索。总之，denumerable 这个词不仅仅是一个数学抽象；它是深入理解各个领域的入口。无论是在数学、计算机科学还是哲学中，denumerable 集合的概念都挑战我们批判性地思考计数、无限和人类知识的局限性。接受这一概念丰富了我们的视角，并鼓励我们更加欣赏周围世界的复杂性。