> Time for the Kleene diagonal argument. Opps, a language L that I dreamt > of does not exist. I have to relax from the condition that M on E_i > always return a number in a finite time. Well, what to return if not a > number ... nothing -> M experiences an infinite loop. > > What a world, ok, my language has to describe total functions from N to > N and as well as strict partial functions from N to N. And it is clear > that I cannot know whether E_i corresponds to a total function or a > strict partial function. f' stands for any function descriable by L. > > 0 --- E_0 ~ f'_0 > 1 --- E_1 ~ f'_1 > 2 --- E_2 ~ f'_2 > 3 --- E_3 ~ f'_3 > .... > .... > > N, E and C are enumerable, moreover obviously effectively enumerable. > Any subset of C is at least enumerable. A subset of C corresponding to > total functions is no effectively enumerable. It cannot be.

Correction: N and E are enumerable, moreover obviously effectively enumerable. C is enumerable and thus any subset of C is at least enumerable. A subset of C corresponding to total functions is not effectively enumerable. It cannot be. Neither C as such is effectively enumerable. It cannot be. Mirek --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---