Function

A function is a many-to-one map between two sets.

Formal definition

Let $D,R \neq \emptyset$ be sets.

If

$$ \forall x \in D: \exists y \in R, f(x)=y $$

Then $f$ is a function of domain $D$ and range $R$, noted as $f: D \to R$.

Example:

$$ f(x)=2x^2, x \in \mathbb{C} $$

is a function, where $f: \mathbb{C} \to \mathbb{C}$