An injective function or injection is 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
\[\inj(X, Y).\]
Note. Injective is also known as one-to-many and left-unique.