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:# Sure, there are tons of simple examples. Whether it's useful to list them is something that might want some thought....
:# Yes, the multiples of 7 form an r.e. set. Write a program that tests the input to see if it's a multiple of 7, and if so outputs 0; otherwise, it goes into an infinite loop. The partial recursive function defined by that program witnesses that the set is r.e. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 18:45, 8 August 2008 (UTC)
::Thank you very much. That helps a bit. Encouraged by that, I'm going to ask another question.
::* Suppose I now have my program that tests the input to see if it is a multiple of 7. If it is, the output is 0. If it is not, the output is 41. BUT the ___domain of this function is all positive integers, not all integers that are multiples of 7. ???
::I didn't mean to suggest including tons of examples but I think a few examples would help a lot. Thanks. [[User:Wanderer57|Wanderer57]] ([[User talk:Wanderer57|talk]]) 19:10, 8 August 2008 (UTC)
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