Mapping/Injective/Definition

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.