commutativity

简明释义

英[kəˌmjuːtəˈtɪvɪti]美[kəmjuːtəˈtɪvɪti]

n. [数] 交换性

英英释义

单词用法

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反义词

例句

1.More complex laws such as commutativity and associativity must be incorporated.

更加复杂的规律如交换性和结合性的合并。

2.We study in this paper the structure of additive mappings on triangular matrix algebras which preserve commutativity.

本文研究了三角矩阵代数上保持交换性的可加映射的结构。

3.We won't run into any problem of non - commutativity in constructing these operators.

在构成这些算符时，我们不会陷入任何非对易性问题中。

4.Finally, on this basis, the proper BCH-algebras of pure high-type quasi-commutativity are given.

最后在此基础上给出了纯高型拟可换的真bch -代数。

5.In this paper, the author gave some commutativity theorems on semi-prime ring with variable identity, which is a generalization related.

给出了满足某可变恒等式的半质环的交换性定理，推广了已有的结论。

6.The so-called " natural " arithmetical operations retain commutativity at the expense of continuity.

所谓的“自然”算术运算以损失连续性的代价保持了交换律。

7.This paper introduced the concept of a union algebra of BCH-algeba and non-negetive BCH-algebra, and discussed quasi-commutativity of (HP) Union algebra.

本文给出了BCH—代数与非负BCH—代数的并代数的概念，并且讨论了拟可换性。

8.In mathematics, the property of commutativity means that the order of operations does not affect the result.

在数学中，交换律的性质意味着操作的顺序不会影响结果。

9.Addition is an example of commutativity; for instance, 3 + 5 is the same as 5 + 3.

加法是一个交换律的例子；例如，3 + 5与5 + 3是相同的。

10.When teaching basic arithmetic, it is important to explain commutativity to help students understand addition and multiplication.

在教授基础算术时，解释交换律是很重要的，以帮助学生理解加法和乘法。

11.In programming, certain functions exhibit commutativity, allowing developers to rearrange parameters without changing the output.

在编程中，某些函数表现出交换律，允许开发人员重新排列参数而不改变输出。

12.The commutativity of multiplication means that a × b equals b × a.

乘法的交换律意味着a × b等于b × a。

作文

Commutativity is a fundamental property in mathematics that describes how certain operations can be performed in any order without affecting the final result. This concept is particularly important in fields such as algebra and arithmetic, where addition and multiplication are commonly used. To illustrate the idea of commutativity (交换律), let us consider a simple example involving addition. If we take two numbers, say 3 and 5, we can add them together in two different ways: 3 + 5 and 5 + 3. In both cases, the result is the same, which is 8. This demonstrates the commutativity (交换律) of addition, meaning that the order in which we add the numbers does not change the outcome. Similarly, multiplication also exhibits commutativity (交换律). For instance, if we multiply 4 by 6, we get 24, and if we reverse the order to multiply 6 by 4, we still arrive at 24. This consistency reinforces the idea that the operation of multiplication is commutative (交换的) as well. However, not all mathematical operations are commutative (交换的). For example, subtraction and division do not possess this property. If we take the numbers 10 and 2, we find that 10 - 2 equals 8, but 2 - 10 equals -8. Clearly, changing the order of the numbers results in different outcomes, thus indicating that subtraction is not commutative (交换的). The same can be said for division; 12 ÷ 3 equals 4, while 3 ÷ 12 equals 0.25, demonstrating a lack of commutativity (交换律) in this operation. Understanding commutativity (交换律) is crucial not only for solving mathematical problems but also for developing logical reasoning skills. It allows mathematicians and students alike to simplify complex expressions and equations by rearranging terms without altering the result. This property is especially useful when dealing with larger sets of numbers or variables, as it provides greater flexibility in computation. In computer science, the concept of commutativity (交换律) plays a significant role in algorithms and data processing. For instance, when performing parallel computations, operations that are commutative (交换的) can be executed simultaneously without concern for the order in which they are processed. This can lead to increased efficiency and faster processing times, which are essential in today’s fast-paced technological environment. In conclusion, commutativity (交换律) is a vital principle in mathematics that impacts various fields, from basic arithmetic to advanced computer algorithms. By recognizing and applying this property, individuals can enhance their problem-solving abilities and improve their understanding of mathematical concepts. Embracing the power of commutativity (交换律) can lead to more efficient calculations and deeper insights into the relationships between numbers and operations. As we continue to explore the world of mathematics, the significance of commutativity (交换律) will undoubtedly remain a cornerstone of our understanding and application of numerical operations.

交换律是数学中的一个基本属性，描述了某些运算可以以任何顺序进行而不影响最终结果的特性。这个概念在代数和算术等领域尤为重要，其中加法和乘法是常用的运算。为了说明commutativity（交换律）的概念，让我们考虑一个简单的加法例子。如果我们取两个数字，比如3和5，我们可以用两种不同的方式将它们相加：3 + 5和5 + 3。在这两种情况下，结果都是8。这证明了加法的commutativity（交换律），意味着我们加数字的顺序不会改变结果。 同样，乘法也表现出commutativity（交换律）。例如，如果我们将4乘以6，我们得到24，而如果我们将顺序反转，将6乘以4，我们仍然得到24。这种一致性进一步加强了乘法是commutative（交换的）这一观点。 然而，并不是所有的数学运算都是commutative（交换的）。例如，减法和除法并不具备这一特性。如果我们取数字10和2，我们发现10 - 2等于8，但2 - 10等于-8。显然，改变数字的顺序会导致不同的结果，因此表明减法不是commutative（交换的）。对于除法也是如此；12 ÷ 3等于4，而3 ÷ 12等于0.25，这表明该运算缺乏commutativity（交换律）。 理解commutativity（交换律）不仅对解决数学问题至关重要，还对发展逻辑推理能力有帮助。它使得数学家和学生能够通过重新排列项而不改变结果来简化复杂的表达式和方程。当处理更大的数字或变量集合时，这一特性尤为有用，因为它提供了更大的计算灵活性。 在计算机科学中，commutativity（交换律）的概念在算法和数据处理方面发挥着重要作用。例如，在执行并行计算时，commutative（交换的）操作可以同时执行，而无需担心它们被处理的顺序。这可以提高效率，加快处理时间，这在当今快速发展的技术环境中至关重要。 总之，commutativity（交换律）是数学中的一个重要原则，影响着从基础算术到高级计算机算法的各个领域。通过识别和应用这一属性，个人可以增强他们的问题解决能力，并改善对数学概念的理解。拥抱commutativity（交换律）的力量可以导致更高效的计算和对数字与运算之间关系的更深刻洞察。随着我们继续探索数学世界，commutativity（交换律）的重要性无疑将继续成为我们理解和应用数值运算的基石。