Mapping/Surjective/Definition

Let ${\displaystyle {}L}$ and ${\displaystyle {}M}$ denote sets, and let

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

be a mapping. Then ${\displaystyle {}F}$ is called surjective if, for every ${\displaystyle {}y\in M}$, there exists at least one element ${\displaystyle {}x\in L}$, such that

${\displaystyle {}F(x)=y\,.}$