Mapping/Definition

Mapping

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

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