one to one correspondence

简明释义

一一对应

英英释义

例句

1.The software requires a one to one correspondence 一一对应 between user accounts and email addresses.

该软件要求用户帐户和电子邮件地址之间有一一对应 一一对应。

2.The teacher explained that there is a one to one correspondence 一一对应 between each student and their assigned desk.

老师解释说，每个学生和他们分配的桌子之间存在一一对应 一一对应。

3.In mathematics, we often establish a one to one correspondence 一一对应 between sets to show they have the same cardinality.

在数学中，我们常常建立集合之间的一一对应 一一对应来证明它们具有相同的基数。

4.In this coding exercise, make sure to create a one to one correspondence 一一对应 between input values and output results.

在这个编码练习中，确保输入值和输出结果之间创建一一对应 一一对应。

5.For the mapping project, we need a one to one correspondence 一一对应 between locations on the map and real-world coordinates.

对于这个映射项目，我们需要地图上的位置和现实世界坐标之间的一一对应 一一对应。

作文

In the field of mathematics, the concept of one to one correspondence is fundamental. It refers to a relationship between two sets where each element in the first set is paired with exactly one unique element in the second set, and vice versa. This concept is crucial for understanding various mathematical principles, including functions, cardinality, and equivalence relations.To illustrate this idea, consider the example of students in a classroom and their assigned lockers. If each student is given a unique locker, we can say that there is a one to one correspondence between the students and the lockers. Each student has access to only one locker, and each locker is assigned to only one student. This ensures that there are no overlaps or omissions, making it easy to track who has which locker.The importance of one to one correspondence extends beyond simple examples like this. In more advanced mathematics, it plays a critical role in defining functions. A function can be thought of as a special kind of relation where every input (or domain) corresponds to exactly one output (or range). For instance, if we have a function f(x) = x + 1, then for every value of x, there is a unique value of f(x). This uniqueness is what makes it a function and is directly tied to the idea of one to one correspondence.Moreover, one to one correspondence is essential when comparing the sizes of different sets. Two sets are said to have the same cardinality if there exists a one to one correspondence between them. For example, consider the set of natural numbers and the set of even numbers. Although it might seem that there are fewer even numbers than natural numbers, we can establish a one to one correspondence by pairing each natural number n with the even number 2n. This demonstrates that both sets are actually infinite and have the same size, despite our initial intuition.Furthermore, the concept of one to one correspondence is not limited to mathematics alone. It finds applications in various fields such as computer science, where data structures like hash tables rely on this principle for efficient data retrieval. In programming, ensuring that each key maps to a unique value is essential for maintaining data integrity and avoiding collisions.In conclusion, the concept of one to one correspondence is a powerful tool in both mathematics and real-world applications. It helps us understand relationships between different sets, defines functions, and allows for meaningful comparisons of sizes between infinite sets. By grasping this concept, we can enhance our problem-solving skills and deepen our understanding of the world around us. Whether in a classroom setting or in the realm of advanced mathematics, the idea of one to one correspondence remains a cornerstone of logical reasoning and analysis.

在数学领域，一一对应的概念是基础性的。它指的是两个集合之间的一种关系，其中第一个集合中的每个元素都与第二个集合中的一个独特元素配对，反之亦然。这个概念对于理解各种数学原理，包括函数、基数和等价关系至关重要。为了说明这一点，考虑一个教室里的学生和他们分配的储物柜的例子。如果每个学生都有一个独特的储物柜，我们可以说学生和储物柜之间存在着一一对应的关系。每个学生只能使用一个储物柜，每个储物柜也只分配给一个学生。这确保了没有重叠或遗漏，使得跟踪谁拥有哪个储物柜变得简单。一一对应的重要性不仅限于简单的例子。在更高级的数学中，它在定义函数时起着关键作用。函数可以被视为一种特殊的关系，其中每个输入（或定义域）对应于唯一的一个输出（或值域）。例如，如果我们有一个函数f(x) = x + 1，那么对于每个x值，都有一个唯一的f(x)值。这个唯一性使其成为函数，并且与一一对应的概念直接相关。此外，当比较不同集合的大小时，一一对应也是必不可少的。如果两个集合之间存在一一对应的关系，则称这两个集合具有相同的基数。例如，考虑自然数集合和偶数集合。尽管看起来偶数的数量少于自然数，但我们可以通过将每个自然数n与偶数2n配对来建立一一对应。这表明这两个集合实际上都是无限的，并且大小相同，尽管我们的直觉可能是相反的。此外，一一对应的概念不仅限于数学。它在计算机科学等多个领域中找到了应用，例如哈希表等数据结构依赖于这一原则以实现高效的数据检索。在编程中，确保每个键映射到唯一值对于维护数据完整性和避免冲突至关重要。总之，一一对应的概念是数学和现实应用中的一种强大工具。它帮助我们理解不同集合之间的关系，定义函数，并允许我们在无限集合之间进行有意义的大小比较。通过掌握这一概念，我们可以增强解决问题的能力，加深对周围世界的理解。无论是在课堂环境还是在高级数学领域，一一对应的思想始终是逻辑推理和分析的基石。