On 13/08/07, Bruno Marchal <marchal.domain.name.hidden> wrote:
> Question to David, and others who could be interested: is the notion
> of enumerable and non enumerable set clear? Can you explain why the set
> of functions from N to N is not enumerable?
Do please remind us. "Off the top of my head", do you mean, by
non-enumerable, arbitrary extensibility by the generation of new
members via diagonalisation?
> Do you people know the difference between ordinal and cardinal (I know
> some knows 'course).
Yes
> I don't think Church thesis can be grasped
> conceptually without the understanding that the class of programmable
> functions is closed for the diagonalization procedure.
Please explain 'programmable functions' and 'closed for the
diagonalisation procedure'.
> Do everyone
> (interested) know how to prove the non enumerability of the subset of N
> by diagonalization?
Which subset do you mean? I've encountered the
diagonalisation/enumerability argument, assuming it's the one I
referred to above.
> Let us go slow and deep so that everybody can understand, once and for
> all. OK?
Definitely OK.
David
>
>
> Le 13-août-07, à 13:29, Kim Jones a écrit :
>
> > where he appears to serve the option of being machine or some other
> > order of being. I must confess that I still don't understand the
> > ontology of angels as opposed to machines but I'm sure his reply
> > contains the reason
>
>
> Don't worry, I will try to explain.
>
>
> Question to David, and others who could be interested: is the notion
> of enumerable and non enumerable set clear? Can you explain why the set
> of functions from N to N is not enumerable?
>
> Just say no, and I go back to Cantor, the one who discussed with the
> pope about the question of naming infinities (!), and indeed the one
> who will discover (or invent) the varieties of infinities.
>
> Do you people know the difference between ordinal and cardinal (I know
> some knows 'course). I don't think Church thesis can be grasped
> conceptually without the understanding that the class of programmable
> functions is closed for the diagonalization procedure. Do everyone
> (interested) know how to prove the non enumerability of the subset of N
> by diagonalization?
>
> Let us go slow and deep so that everybody can understand, once and for
> all. OK?
>
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
> >
>
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Received on Mon Aug 13 2007 - 11:16:50 PDT