Consider the set $S = \{ \sqrt n \mid n \in \Bbb N_0\}$
This is a countable set certainly as we can produce a simple one-to-one function for this set to natural numbers. But I want to do it another way. There is a theorem that given an alphabet set the language generated over that alphabet is countable. So for using this theorem, I have to come up with an alphabet for $S$