在数学里，恒等函数为一无任何作用的函数：它总是传回和其输入值相同的函数值。换句话说，恒等函数为函数f(x) = x。

设M为一集合，于M上的恒等函数f被定义于一具有定义域和陪域M的函数，其对任一M内的元素x，会有f(x)=x的关系。

于M上的恒等函数f通常标记为id_M或1_M。

In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. In equations, the function is given by f(x) = x.