Any non-regular language is the countable union of singletons, and each singleton is regular.
I am having trouble understanding why this statement is false. The explanation given to us explains that since A could be infinite, that's the reason why the union of all sets can't be guaranteed to be regular. I'm trying to think of an example of a language that isn't regular, such as the language of strings where the number of a's matches the number of b's. Is there a way I could provide a set of regular languages A that could use union to create this language? Any help with understanding why this is the case would be appreciated.