Prove or disprove or this statement:

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

Can someone help?

  • 1
    $\begingroup$ Can you represent a non-regular language as an infinite union of finite languages? $\endgroup$
    – ttnick
    Apr 25 at 15:18
  • 2
    $\begingroup$ Think about $L_k = \{a^kb^k\}$ (the language with exactly one word $a^kb^k$). $\endgroup$
    – Nathaniel
    Apr 25 at 15:34
  • $\begingroup$ @ttnick I think no. Am I right? $\endgroup$
    – codetime1
    Apr 25 at 15:57

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


Not the answer you're looking for? Browse other questions tagged or ask your own question.