# Mapping/Injective/Definition

Injective

Let and denote sets, and let

be a
mapping.
Then is called * injective*, if for two different elements
,
also
and
are different.

Injective

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

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

be a
mapping.
Then ${}F$ is called * injective*, if for two different elements
${}x,x'\in L$,
also
${}F(x)$ and ${}F(x')$
are different.