injective function
单射函数
injective mapping
单射映射
injective relation
单射关系
injective homomorphism
单射同态
injective type
单射类型
injective property
单射性质
injective set
单射集合
injective design
单射设计
injective sequence
单射序列
injective algorithm
单射算法
an injective function maps distinct elements to distinct images.
一个单射函数将不同的元素映射到不同的像。
to prove that a function is injective, we need to show that if f(a) = f(b), then a must equal b.
要证明一个函数是单射，我们需要证明如果f(a) = f(b)，那么a必须等于b。
injective mappings are essential in many areas of mathematics.
单射映射在许多数学领域中是必不可少的。
the concept of injective functions is fundamental in linear algebra.
单射函数的概念在线性代数中是基础。
in computer science, injective functions can help optimize data retrieval.
在计算机科学中，单射函数可以帮助优化数据检索。
understanding injective relationships can aid in database design.
理解单射关系可以帮助数据库设计。
injective functions are often used in cryptography for secure communication.
单射函数常用于密码学以确保安全通信。
to construct an injective function, one must ensure that each input has a unique output.
要构造一个单射函数，必须确保每个输入都有一个唯一的输出。
injective functions can be visualized using graphs to show their properties.
可以通过图形可视化单射函数，以展示其属性。
many algorithms rely on the injective nature of certain functions for efficiency.
许多算法依赖于某些函数的单射性质以提高效率。
injective function
单射函数
injective mapping
单射映射
injective relation
单射关系
injective homomorphism
单射同态
injective type
单射类型
injective property
单射性质
injective set
单射集合
injective design
单射设计
injective sequence
单射序列
injective algorithm
单射算法
an injective function maps distinct elements to distinct images.
一个单射函数将不同的元素映射到不同的像。
to prove that a function is injective, we need to show that if f(a) = f(b), then a must equal b.
要证明一个函数是单射，我们需要证明如果f(a) = f(b)，那么a必须等于b。
injective mappings are essential in many areas of mathematics.
单射映射在许多数学领域中是必不可少的。
the concept of injective functions is fundamental in linear algebra.
单射函数的概念在线性代数中是基础。
in computer science, injective functions can help optimize data retrieval.
在计算机科学中，单射函数可以帮助优化数据检索。
understanding injective relationships can aid in database design.
理解单射关系可以帮助数据库设计。
injective functions are often used in cryptography for secure communication.
单射函数常用于密码学以确保安全通信。
to construct an injective function, one must ensure that each input has a unique output.
要构造一个单射函数，必须确保每个输入都有一个唯一的输出。
injective functions can be visualized using graphs to show their properties.
可以通过图形可视化单射函数，以展示其属性。
many algorithms rely on the injective nature of certain functions for efficiency.
许多算法依赖于某些函数的单射性质以提高效率。
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