As in the topic, if I have a language with alphabet {a}, does a^n, where n > 1000 a regular language? I am confused. I tried to apply the Pumping Lemma here, and I am unsure of the result. From one side I can see that if I pump out from a^1001 one of a's, then I will have a^1000 which does not belong to L. On the other side I couldn't find any examples of such cases, so maybe my reasoning is wrong.
It's regular. Consider the regular expression a{1001}a* where a{1001} is a string of 1001 a's.