One-to-One Correspondance

one-to-one function, onto

A function $f : A \to B$ is one-to-one (1-1) (injective) if $a_{1} \neq a_{2}$ in $A$ implies that $f (a_{1}) \neq f (a_{2})$ in $B$ . The function $f$ is onto (surjective) if, given any $b \in B$ , it is possible to find an element $a \in A$ for which $f (a) = b$ .