A bijection / one-to-one correspondence is a function that is both an injection and an surjection, i.e. an injection $f:X\to Y$ such that $\ran f=Y$.
The set of all bijections from $X$ onto $Y$ is denoted by $\bij(X,Y)$.
A bijection / one-to-one correspondence is a function that is both an injection and an surjection, i.e. an injection $f:X\to Y$ such that $\ran f=Y$.
The set of all bijections from $X$ onto $Y$ is denoted by $\bij(X,Y)$.