Mapping/Definition

Let ${\displaystyle {}L}$ and ${\displaystyle {}M}$ denote sets. A mapping ${\displaystyle {}F}$ from ${\displaystyle {}L}$ to ${\displaystyle {}M}$ is given by assigning to every element of the set ${\displaystyle {}L}$ exactly one element of the set ${\displaystyle {}M}$. The unique element that is assigned to ${\displaystyle {}x\in L}$ is denoted by ${\displaystyle {}F(x)}$. For the mapping as a whole, we write

${\displaystyle F\colon L\longrightarrow M,x\longmapsto F(x).}$