For this question you are not allowed to invoke any set that is known to be uncountable (such as subsets of $\mathbb{R}$) in your answer. Let $A = \{a, b, c\}$. Consider the set of functions $F$ whose elements are functions $f : \mathbb{Z}^+ → A$. Using diagonalization, prove that $F$ is uncountable.
For this I think I need to do cantors diaganolization but I'm not sure what "$f : \mathbb{Z}^+ → A$" means and how to start it off
Thanks