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