An injection / one-to-one function is a function that is injective, i.e. a function $f$ such that
\[\forall x,y\in\dom f :\enspace f(x)=f(y) \enspace\rimp\enspace x=y.\]The set of all injections from $X$ to $Y$ is denoted by $\inj(X,Y)$.
$\varnothing$ is an injection.