surjective

简明释义

英[/sɜrˈdʒɛktɪv/]美[/sɜrˈdʒɛktɪv/]

adj. 满射的

英英释义

单词用法

同义词

反义词

例句

1.We also prove that every 2-local isomety of UHF algebra is linear by studying the structure of the surjective isometry on UHF algebra.

对于UHF代数上满等距的结构，还证明了UHF代数上的2局部（满线性）等距是线性的。

2.F is strategy-proof and surjective.

是防止策略操纵的且F是满的。

3.We also prove that every 2-local isomety of UHF algebra is linear by studying the structure of the surjective isometry on UHF algebra.

对于UHF代数上满等距的结构，还证明了UHF代数上的2局部（满线性）等距是线性的。

4.A surjective 满射 function guarantees that no output is left unused, which is crucial in certain applications.

一个surjective 满射函数保证没有输出被忽略，这在某些应用中至关重要。

5.In mathematics, a function is called surjective 满射 if every element in the codomain is mapped to by at least one element from the domain.

在数学中，如果一个函数的每个值都至少由定义域中的一个元素映射到，则该函数被称为surjective 满射。

6.In computer science, understanding whether a function is surjective 满射 can help in designing algorithms that require complete coverage of a set.

在计算机科学中，了解一个函数是否是surjective 满射可以帮助设计需要完全覆盖集合的算法。

7.To prove that a function is surjective 满射, we need to show that for every element in the output set, there exists a corresponding input.

要证明一个函数是surjective 满射，我们需要展示输出集中每个元素都有对应的输入。

8.The mapping defined by this equation is surjective 满射, as every possible output can be achieved.

由这个方程定义的映射是surjective 满射，因为可以实现每一个可能的输出。

作文

In the realm of mathematics, particularly in the field of set theory and functions, the term surjective refers to a specific type of function that has a unique property. A function is considered surjective (或称为“满射”) if every element in the codomain has at least one pre-image in the domain. This means that for every output value, there exists at least one input value that maps to it. Understanding this concept is crucial for anyone studying advanced mathematics, as it lays the foundation for more complex topics such as bijections and inverses.To illustrate the idea of a surjective function, let’s consider a simple example. Suppose we have a function f: {1, 2, 3} → {a, b}. If we define the function such that f(1) = a, f(2) = a, and f(3) = b, we can see that both elements 'a' and 'b' in the codomain {a, b} are covered by the function. Here, 'a' has two pre-images (1 and 2), while 'b' has one pre-image (3). Thus, this function is surjective because every element in the codomain has a corresponding element in the domain.On the other hand, if we modify the function to f: {1, 2} → {a, b} with f(1) = a and f(2) = a, we notice that 'b' in the codomain does not have any pre-image in the domain. Hence, this function is not surjective because it fails to map to every element in the codomain.The significance of surjective functions extends beyond mere definitions; they play a vital role in many areas of mathematics, including algebra and topology. Surjective functions ensure that certain properties hold true when dealing with transformations and mappings between different sets. For instance, in linear algebra, understanding whether a linear transformation is surjective can help determine whether the system of equations has a solution for every possible outcome.Moreover, the concept of surjective functions can be applied in real-world scenarios. For example, consider a situation where a company wants to assign employees to projects. If each project must have at least one employee assigned to it, the assignment process can be modeled using a surjective function. Each project represents an element in the codomain, and each employee represents an element in the domain. To ensure that every project receives attention, the assignment must be surjective.In conclusion, the term surjective encapsulates a fundamental aspect of mathematical functions that is essential for deeper comprehension of functional relationships. By recognizing the importance of surjective mappings, students and professionals alike can better navigate through the complexities of mathematics. Whether in theoretical contexts or practical applications, understanding surjective functions empowers individuals to solve problems effectively and efficiently. As we continue to explore the vast landscape of mathematics, let us not forget the significance of such concepts, which serve as building blocks for our understanding of the world around us.

在数学领域，尤其是在集合论和函数的研究中，术语surjective（或称为“满射”）指的是具有特定性质的函数。如果一个函数被认为是surjective，这意味着在其值域中的每个元素至少有一个对应的原像在定义域中。这意味着对于每个输出值，都存在至少一个输入值映射到它。理解这一概念对任何学习高级数学的人来说都是至关重要的，因为它为更复杂的主题如双射和反函数奠定了基础。为了说明surjective函数的概念，我们考虑一个简单的例子。假设我们有一个函数f: {1, 2, 3} → {a, b}。如果我们将这个函数定义为f(1) = a，f(2) = a，f(3) = b，我们可以看到在值域{a, b}中的两个元素'a'和'b'都被这个函数覆盖。在这里，'a'有两个原像（1和2），而'b'有一个原像（3）。因此，这个函数是surjective的，因为值域中的每个元素都有一个对应的定义域中的元素。另一方面，如果我们将函数修改为f: {1, 2} → {a, b}，并且f(1) = a和f(2) = a，我们会注意到值域中的'b'没有任何原像在定义域中。因此，这个函数不是surjective的，因为它未能映射到值域中的每个元素。surjective函数的重要性超越了简单的定义；它们在代数和拓扑等许多数学领域中发挥着重要作用。满射函数确保在处理不同集合之间的变换和映射时某些属性保持真实。例如，在线性代数中，了解线性变换是否是surjective可以帮助确定方程组是否对每个可能的结果都有解。此外，surjective函数的概念还可以应用于现实场景。例如，考虑一个公司希望将员工分配到项目中的情况。如果每个项目必须至少有一个员工分配给它，那么分配过程可以用surjective函数进行建模。每个项目代表值域中的一个元素，而每个员工代表定义域中的一个元素。为了确保每个项目都得到关注，分配必须是surjective的。总之，术语surjective概括了数学函数的一个基本方面，对于更深入地理解函数关系至关重要。通过认识到surjective映射的重要性，学生和专业人士可以更好地应对数学的复杂性。无论是在理论背景还是实际应用中，理解surjective函数使个人能够有效和高效地解决问题。在我们继续探索广阔的数学领域时，不要忘记这些概念的重要性，它们作为我们理解周围世界的基石。