Is the union of computable enumerable sets computably enumerable Let $\{A_n : n \in \mathbb{N}\}$ be a collection of c.e. (computably enumerable) sets. Is $\bigcup_n A_n$ c.e.?
That is, is the union of c.e. sets c.e.? Otherwise, under what conditions will this be true?
Every language can be written as a countable union of singletons $\{x\}$.
On the other hand, the union of finitely many c.e. languages is c.e.