# Mapping/Surjective/Definition

Surjective

Let and denote sets, and let

be a
mapping.
Then is called * surjective*, if for every
,
there exists at least one element
,
such that

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

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