A surjective function / surjection is a right-total function, i.e. a function $f:X\to Y$ such that for all $y\in Y$,
\[\exists x\in X : f(x) = y.\]In other words, $\ran f=Y$.
The set of all surjections from $X$ onto $Y$ is denoted by
\[\sur(X,Y).\]
- Synonym of surjection: onto function