# Complexity classes closed under finite union and intersection, why not infinite union and intersection?

All "nice" Complexity classes are closed under finite union and intersection. (By "nice" I mean ones with complete problems or leaf languages, e.g. P, NP, PSPACE, etc.)

But such classes are not closed under infinite union and intersection. Why?

• I edited the question to improve it. – 6005 Apr 29 '20 at 4:32

Consider the "singleton" languages: $$L=\{w\}$$ for some fixed word $$w$$. (e.g., the language $$L=\{00010100\}$$ would be a singleton language) Most "nice" complexity classes include the singleton languages.