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Prove or disprove or this statement:

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

Can someone help?

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    $\begingroup$ Can you represent a non-regular language as an infinite union of finite languages? $\endgroup$ – ttnick Apr 25 at 15:18
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    $\begingroup$ 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
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Every language is a union of infinitely many regular languages: $$ L = \bigcup_{w \in L} \{w\}. $$

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