transfinite

简明释义

英[trænsˈfaɪnaɪt]美[trænsˈfaɪnaɪt]

adj. [数] 超限的；无穷的；无限的

英英释义

单词用法

同义词

反义词

例句

1.This paper proposes an modified continuous transfinite interpolation method for automatic grid generation of axisymmetric BEM in terms of previous automatic mesh generation work in FEM.

本文在有限元法的前处理工作基础上，提出了回转体非线性边界元自动前处理的改进插值法。

2.The research consists of several parts which are listed below. Finally, from the view of design, using SATWE and PMSAP, the paper analyzes a transfinite split-level structure.

最后从设计角度出发，用SAT WE及PMSAP对某一超限错层剪力墙实例进行了分析及计算。

3.They can continue by transfinite induction.

利用超限归纳法，他们可继续下去。

4.The emulation experiment indicated that the controlling effect was well, namely little transfinite regulation and good robustness, the shape of strip could be controlled on-line and intelligently.

仿真实验表明，控制效果相当好，其超调小、鲁棒性强，达到了板形在线智能控制之目的。

5.The emulation experiment indicated that the controlling effect was well, namely little transfinite regulation and good robustness, the shape of strip could be controlled on-line and intelligently.

仿真实验表明，控制效果相当好，其超调小、鲁棒性强，达到了板形在线智能控制之目的。

6.Cargo types: Pu goods, dangerous goods, frozen goods, frozen dangerous goods, valuables, transfinite goods.

货种：普货，危险品，冷冻品，冷冻危险品，贵重物品，超限货物。

7.Using transfinite 超限的 induction, we can prove statements about all ordinal numbers.

通过使用transfinite 超限的 归纳法，我们可以证明关于所有序数的陈述。

8.A transfinite 超限的 number can be used to describe the size of certain infinite sets.

一个transfinite 超限的 数字可以用来描述某些无限集合的大小。

9.The mathematician introduced a transfinite 超限的 sequence to illustrate the properties of infinite sets.

这位数学家引入了一个transfinite 超限的 序列，以说明无限集合的性质。

10.In set theory, the concept of transfinite 超限的 numbers extends beyond the finite integers.

在集合论中，transfinite 超限的 数字的概念超出了有限整数的范围。

11.The theory of transfinite 超限的 cardinals is essential in understanding different sizes of infinity.

超限基数理论对于理解不同大小的无限性至关重要。

作文

The concept of transfinite numbers is a fascinating area of mathematics that extends our understanding of infinity. Traditionally, we think of numbers as finite entities, those that can be counted or measured. However, mathematicians like Georg Cantor revolutionized this perspective by introducing the idea of transfinite numbers, which allows us to explore different sizes and types of infinity. This essay will delve into the significance of transfinite numbers and their implications in various fields.To begin with, let us define what transfinite means. The term refers to quantities that are larger than any finite number, yet still defined within a mathematical framework. Cantor distinguished between different levels of infinity, notably through his work on sets. He introduced the concept of cardinality, which measures the size of sets, even when they are infinite. For instance, the set of natural numbers is infinite, but Cantor showed that the set of real numbers is 'larger' than the set of natural numbers. This leads us to the first type of transfinite number: aleph-null (ℵ₀), which represents the smallest infinity, the size of the set of all natural numbers.One of the most intriguing aspects of transfinite numbers is their ability to challenge our conventional understanding of mathematics. For example, Cantor's diagonal argument demonstrates that there are more real numbers than natural numbers, implying that not all infinities are equal. This revelation has profound implications in fields such as set theory, topology, and even computer science, where concepts of infinity play a crucial role in algorithms and data structures.Moreover, the application of transfinite numbers extends beyond pure mathematics. In philosophy, the notion of infinity has been debated for centuries, and the introduction of transfinite numbers adds a new dimension to these discussions. Philosophers ponder the nature of reality and existence, and the concept of transfinite numbers invites us to reconsider the boundaries of what we perceive as possible.In addition, transfinite numbers have practical applications in computer science, particularly in the realm of theoretical computer science. When dealing with algorithms that involve infinite loops or recursive functions, understanding transfinite concepts can provide insights into the behavior of these systems. For instance, the analysis of algorithms often requires an understanding of limits and convergence, areas where transfinite numbers become relevant.Furthermore, the exploration of transfinite numbers has led to the development of various mathematical theories, such as ordinal numbers and the continuum hypothesis. Ordinal numbers extend the idea of counting beyond finite numbers, allowing us to describe the order type of well-ordered sets. The continuum hypothesis, on the other hand, questions whether there is a set whose cardinality is strictly between that of the integers and the real numbers, further illustrating the complexities inherent in transfinite mathematics.In conclusion, the study of transfinite numbers opens up a world of possibilities that challenges our traditional views of mathematics and infinity. By understanding transfinite concepts, we gain deeper insights into the nature of mathematics itself and its applications across various disciplines. The implications of transfinite numbers reach far beyond abstract theory; they influence our understanding of reality, computation, and the very fabric of mathematical thought. As we continue to explore these ideas, we may uncover even more about the infinite landscapes that transfinite numbers reveal, ultimately enriching our comprehension of both mathematics and the universe around us.

超限数的概念是数学中一个迷人的领域，它扩展了我们对无穷大的理解。传统上，我们认为数字是有限的实体，可以被计数或测量。然而，像乔治·康托尔这样的数学家通过引入超限数的概念，彻底改变了这种观点，使我们能够探索不同大小和类型的无穷大。本文将深入探讨超限数的重要性及其在各个领域的影响。首先，让我们定义一下什么是超限。这个术语指的是比任何有限数字都要大的量，但仍然在一个数学框架内定义。康托尔区分了不同级别的无穷大，特别是通过他对集合的研究。他引入了基数的概念，用于衡量集合的大小，即使它们是无限的。例如，自然数的集合是无限的，但康托尔展示了实数的集合比自然数的集合“更大”。这使我们得出了第一种超限数：阿列夫零（ℵ₀），它代表最小的无穷大，即所有自然数的大小。超限数最有趣的方面之一是它们挑战我们传统的数学理解。例如，康托尔的对角线证明表明，实数的数量比自然数的数量要多，这意味着并非所有无穷大都是相等的。这一发现对集合论、拓扑学甚至计算机科学等领域具有深远的影响，在这些领域中，无穷大的概念发挥着重要作用。此外，超限数的应用超越了纯数学。在哲学中，无穷大的概念已经被讨论了几个世纪，而超限数的引入为这些讨论增添了新的维度。哲学家们思考现实和存在的本质，而超限数的概念促使我们重新考虑我们所认为的可能性的边界。此外，超限数在计算机科学中也有实际应用，特别是在理论计算机科学领域。当处理涉及无限循环或递归函数的算法时，理解超限概念可以为我们提供对这些系统行为的洞察。例如，算法分析通常需要理解极限和收敛性，而这些领域与超限数密切相关。此外，超限数的探索导致了各种数学理论的发展，如序数和连续统假设。序数将计数的概念扩展到有限数字之外，使我们能够描述良序集合的顺序类型。另一方面，连续统假设则质疑是否存在一个基数严格介于整数和实数之间的集合，进一步说明了超限数学中固有的复杂性。总之，超限数的研究打开了一扇可能性的大门，挑战了我们对数学和无穷大的传统看法。通过理解超限概念，我们获得了对数学本质及其在各个学科中的应用的更深刻见解。超限数的影响远远超出了抽象理论；它们影响着我们对现实、计算和数学思想本质的理解。随着我们继续探索这些思想，我们可能会揭示更多关于超限数所揭示的无限景观的知识，最终丰富我们对数学和周围宇宙的理解。