双射

The function f is a bijection if it is both one-to-one and onto.
函数f是双射，如果它是唯一对应的，并且是满射的。
There exists a bijection between the set of natural numbers and the set of even numbers.
存在一个将自然数集与偶数集进行一一对应的关系。
The mapping from points in the plane to their polar coordinates is a bijection.
平面上点到它们极坐标的映射是一个双射。
The set of all permutations on n elements forms a group under composition, with each permutation being a bijection.
所有n元素的排列在复合下形成一个群，每个排列都是一个双射。
In graph theory, an isomorphism between two graphs is a bijection that preserves adjacency.
在图论中，两个图之间的同构是一个保持相邻关系的双射。
The Cantor pairing function is a bijection from the set of pairs of natural numbers to the set of natural numbers.
卡内塔配对函数是从一对自然数的集合到自然数集合的双射。
The exponential function e^x is a bijection from the real numbers to the positive real numbers.
指数函数e^x是从实数到正实数的双射。
A bijection can be used to show that the set of rational numbers is countable.
可以使用双射来证明有理数集是可数的。
The concept of a bijection is fundamental in establishing the cardinality of infinite sets.
双射的概念在确定无限集的基数时是基础性的。
In set theory, a bijection between two sets indicates that they have the same cardinality.
在集合论中，两个集之间存在双射表示它们具有相同的基数。