A map $f$ is called injective if it never maps distinct element to the same element, i.e. from $f(x)=f(x')$ follows that $x=x'$. A map $f\colon X\to Y$ is called surjective if each element $y\in Y$ has at least one preimage, i.e. $f^{-1}(y)\ne\emptyset$ for any $y\in Y$.