function

A function $f$ (sometimes called a mapping) is the relation $f\subseteq A\times B$ with the property that for each $x\in A$, there is only one $y\in B$ such that $⟨x,y⟩\in f$, that is, each element in the domain of $f$ is only mapped to one element in the image or codomain.

A function can have multiple arguments, which is represented as an ordered pair / set. For instance, a two-argument function $f$ that simply multiplies its arguments is notated as $f:\mathbb{R}\times \mathbb{R}\to \mathbb{R}$. In general, a $k$-ary function $f$ has a domain that is the Cartesian product of $k$ sets, so we can write $f(x_1,\dots ,x_k)$ as $f(⟨x_1,\dots ,x_k⟩)$.