  == Godel number ==  You just edited that article.  Unfortunately, the definition is completely screwy; it makes no sense to say that a function from S to N is computable, if elements of S have not already been assigned Godel numbers.  And a computable function cannot output random elements, unless they have been assigned Godel numbers.  So neither the function f nor its inverse could possibly be computable if S is anything other than the natural numbers.   If you are interested in fixing the article, please feel free (nobody else has stepped up, and I am putting it off). There is already some discussion on the talk page in the section Definition. I'm writing because minor changes you make might get lost if and when the article is rewritten, and that would be a waste of your time.  ·  