Mapsto notation

In mathematics, the arrow \(\mapsto\) (which in LaTeX is called “\mapsto”) is used to describe what a function does to an arbitrary input. It is commonly used in combination with colon-to notation, which describes what a function’s domain and codomain are.

By itself, \(\mapsto\) can be used to describe a function without naming it, and so is a way to describe anonymous functions in mathematics.


The function \(f(x) = x^2\) from the real numbers to the real numbers can be described using a combination of colon-to notation and mapsto notation as

$$f : \mathbb{R} \to \mathbb{R}$$
$$x \mapsto x^2.$$

In one line, although this is less common,

$$f : \mathbb{R} \ni x \mapsto x^2 \in \mathbb{R}.$$

(see in notation).