I need to solve this exercise:
Consider $\psi: f\in \mathbb Z^{\mathbb Z} \mapsto f(2) \in \mathbb Z$. Is $\psi$ injective? Is it surjective?
I've never had to work with functions as elements before, so I am a bit confused. Does $f(2)$ mean a function $f$ having $2$ as parameter? Proving $\psi$ to be an injection means that I have to find a $g$ function so that $\psi(f)=\psi(g) \Leftrightarrow f=g$. How do I do that? And how do I prove that $\exists g \in \mathbb Z^{\mathbb Z} : \; \psi(g)=f(2)$? A nudge in the right direction would be really appreciated.