数学中，一个由集合X映射至集合Y的函数，若对每一在Y内的y，存在唯一一个在X内的x与其对应，则此函数为对射函数。

换句话说，f为双射的若其为两集合间的一一对应，亦即同时为单射和满射。

例如，由整数集合至的函数succ，其将每一个整数x链接至整数succ(x)=x+1，这是一个双射函数；再看一个例子，函数sumdif，其将每一对实数(x,y)链接至sumdif(x,y) = (x + y, x − y)，这也是个双射函数。

一双射函数亦简称为双射（英语：bijection）或置换。后者一般较常使用在X=Y时。以由X至Y的所有双射组成的集合标记为XY.

In mathematics, a bijection, bijective function or one-to-one correspondence is a function between the elements of two sets, where every element of one set is paired with exactly one element of the other set, and every element of the other set is paired with exactly one element of the first set. There are no unpaired elements. In mathematical terms, a bijective function f: X → Y is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y.