> 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.

##
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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
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