# Is the union of infinitely many regular languages always regular? [duplicate]

Prove or disprove or this statement:

The union of an infinite number of regular languages is regular.

Can someone help?

• Can you represent a non-regular language as an infinite union of finite languages? Apr 25 at 15:18
• Think about $L_k = \{a^kb^k\}$ (the language with exactly one word $a^kb^k$). Apr 25 at 15:34
• @ttnick I think no. Am I right? Apr 25 at 15:57

Every language is a union of infinitely many regular languages: $$L = \bigcup_{w \in L} \{w\}.$$