denumerably

简明释义

英[dɪˈnjuː.mə.rə.bli]美[dɪˈnuː.mə.rə.bli]

可数地

英英释义

单词用法

同义词

反义词

例句

1.The universe of discourse consists of denumerably many individuals.

话语世界由许多个可数的个体组成。

2.The universe of discourse consists of denumerably many individuals.

话语世界由许多个可数的个体组成。

3.In mathematics, we often deal with denumerably infinite sets when discussing concepts like countability.

在数学中，我们经常处理可数无限集合，特别是在讨论可数性等概念时。

4.The set of natural numbers is denumerably infinite, meaning it can be put into a one-to-one correspondence with the integers.

自然数的集合是可数无限的，意味着它可以与整数建立一一对应关系。

5.Understanding denumerably infinite sets is crucial for advanced topics in set theory.

理解可数无限集合对于集合论中的高级主题至关重要。

6.A denumerably infinite set has the same cardinality as the set of all integers.

一个可数无限的集合与所有整数的集合具有相同的基数。

7.The rational numbers are denumerably infinite, as they can be listed in a sequence.

有理数是可数无限的，因为它们可以按顺序列出。

作文

In the realm of mathematics, particularly in set theory, the concept of infinity is often explored through various types of infinite sets. One such classification is that of denumerably infinite sets, which are sets that can be put into a one-to-one correspondence with the natural numbers. This means that the elements of a denumerably infinite set can be counted, even though they extend indefinitely. A classic example of a denumerably infinite set is the set of all integers, which includes both positive and negative whole numbers as well as zero.Understanding denumerably infinite sets requires a grasp of the distinction between different sizes of infinity. For instance, while the set of natural numbers is denumerably infinite, the set of real numbers is considered uncountably infinite. This difference highlights the fascinating nature of infinity and how it can manifest in various forms.The implications of denumerably infinite sets extend beyond pure mathematics and into fields such as computer science and philosophy. In computer science, for example, algorithms often operate under the assumption that they can process denumerably infinite sequences, even if in practice, they can only handle finite inputs. This raises interesting questions about computation and the limits of what can be achieved with algorithms.Philosophically, the concept of denumerably infinite sets challenges our understanding of the universe and existence itself. If we accept that there are denumerably infinite entities, it leads to debates about the nature of reality and whether infinities can truly exist in the physical world. Such discussions can be seen in the works of various thinkers who pondered the implications of infinity on existence and knowledge.Moreover, in practical applications, the idea of denumerably infinite sets can be utilized in statistics and probability theory. When dealing with random variables or outcomes, researchers often assume a denumerably infinite number of possibilities to simplify calculations and models. This assumption can lead to effective predictions and analyses, despite the inherent complexities involved in working with infinite sets.In conclusion, the term denumerably refers to a specific type of infinity that is countable and can be associated with the natural numbers. Its significance spans across mathematics, computer science, philosophy, and practical applications in statistics. By exploring the concept of denumerably infinite sets, we gain deeper insights into the nature of infinity and its relevance in various disciplines. As we continue to study these ideas, we uncover more about the intricate relationships between numbers, computation, and the philosophical implications of infinite existence.

在数学领域，特别是在集合论中，关于无穷大的概念常常通过各种类型的无限集合进行探讨。其中一个分类是可列无限集合，即可以与自然数建立一对一对应关系的集合。这意味着可列无限集合的元素可以被计数，尽管它们无穷无尽。一个经典的可列无限集合的例子是所有整数的集合，其中包括正整数、负整数以及零。理解可列无限集合需要掌握不同大小的无穷大之间的区别。例如，虽然自然数的集合是可列无限的，但实数的集合被认为是不可列无限的。这种差异突显了无穷大的迷人性质及其在不同形式中的表现。可列无限集合的含义超越了纯数学，延伸到计算机科学和哲学等领域。例如，在计算机科学中，算法通常假设它们可以处理可列无限序列，即使在实践中，它们只能处理有限输入。这引发了有关计算和算法所能实现的限制的有趣问题。在哲学上，可列无限集合的概念挑战了我们对宇宙和存在本身的理解。如果我们接受存在可列无限实体的观点，就会引发关于现实的性质以及无穷大是否可以在物理世界中真正存在的辩论。这类讨论可以在各种思考者的著作中看到，他们思考无穷大对存在和知识的影响。此外，在实际应用中，可列无限集合的概念可以在统计和概率论中得到利用。当处理随机变量或结果时，研究人员通常假设存在可列无限种可能性，以简化计算和模型。这一假设可以导致有效的预测和分析，尽管处理无限集合固有的复杂性。总之，术语可列无限指的是一种特定类型的无穷大，它是可计数的，并且可以与自然数相关联。它的重要性横跨数学、计算机科学、哲学以及统计等实际应用。通过探索可列无限集合的概念，我们获得了对无穷大的本质及其在各个学科中相关性的更深入见解。随着我们继续研究这些思想，我们揭示了数字、计算和无限存在的哲学意义之间错综复杂的关系。