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I'm trying to figure out how to prove or disprove the following statement:

Infinite union of recursive languages is recursively enumerable.

I know how to prove that infinite union of regular languages is not recursive, but I can't figure out how to prove the statement above. Intuition is telling me that the statement is true, but I'm not sure. Does anybody know how would I go about it?

Any help is greatly appreciated.

Raphael
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flashburn
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1 Answers1

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Choose an arbitrary language $L$ that is not RE. Denote $L_w=\{w\}$ the language containing a single word $w$. Clearly, $L=\bigcup_{w\in L} L_w$ is a union of infinitely many regular and recursive languages.

avakar
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