Is the set of all finite and countably infinite sequences over $\{0,1\}$ countable?
From my analysis, I think it is countable. I think of this as the set of all strings from a finite alphabet $\Sigma=\{0,1\}$, hence $\Sigma^*$. (is this a good assumption?).
I later show that I can count each string in the following order: $0$,$1$ (length $1$), $00$, $01$, $10$, $11$ (length $2$) and so on.
However, I am very confused from the initial requirement "finite and countably infinite sequences". Does my method account for the countably infinite strings?