Mapping/Surjective/Definition

Surjective

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

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

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

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