I'm going through my textbook here and a lot of the examples show surjective functions that only map, say $$ \mathbb{R} \rightarrow \mathbb{R} $$
But it just occurred to me what if I wanted to come up with a function that is surjective but more restrictive? Like Odd -> Odd? I'm not sure why but I'm having some real trouble coming up with one and it's bugging me. Where would I even start?
On any set $S$, the function from $S$ to $S$ defined by
$$f(x)=x$$
is a surjection (in fact, it is also a bijection) from $S$ to $S$.