Le 30-mai-06, à 19:13, Tom Caylor wrote :
>
>> From what you've said about dovetailing before, you don't have to have
> just a single sequence in order to dovetail. You can jump among
> multiple sequences. I have yet to understand how you could dovetail on
> something that is not effective. T
Hal Finney wrote:
>Jesse Mazer writes:
> > The dovetailer is only supposed to generate all *computable* functions
> > though, correct? And the diagonalization of the (countable) set of all
> > computable functions would not itself be computable.
>
>The dovetailer I know does not seem relevant to
Le Mercredi 31 Mai 2006 00:21, Hal Finney a écrit :
> The dovetailer I know does not seem relevant to this discussion about
> functions. It generates programs, not functions. For example, it
> generates all 1 bit programs and runs each for one cycle; then generates
> all 2 bit programs and runs
Jesse Mazer writes:
> The dovetailer is only supposed to generate all *computable* functions
> though, correct? And the diagonalization of the (countable) set of all
> computable functions would not itself be computable.
The dovetailer I know does not seem relevant to this discussion about
func
George Levy wrote:
>
>
>Bruno Marchal wrote:
>
> >Meanwhile, I
> >would like to ask George and the others if they have a good
> >understanding of the present thread, that is on the fact that growing
> >functions has been well defined, that each sequence of such functions
> >are well defined, and
Bruno Marchal wrote:
>Meanwhile, I
>would like to ask George and the others if they have a good
>understanding of the present thread, that is on the fact that growing
>functions has been well defined, that each sequence of such functions
>are well defined, and each diagonalisation defines qui
Quentin Anciaux wrote:
> Hi,
>
> >From what you've said about dovetailing before, you don't have to have
> >
> > just a single sequence in order to dovetail. You can jump among
> > multiple sequences. I have yet to understand how you could dovetail on
> > something that is not effective.
>
> I
Hi,
>From what you've said about dovetailing before, you don't have to have
>
> just a single sequence in order to dovetail. You can jump among
> multiple sequences. I have yet to understand how you could dovetail on
> something that is not effective.
I think dovetailing is possible because
Tom Caylor wrote:
> It sounds like the cute theorem says that you can keep dividing up the
> natural numbers like this forever.
>
Oops. I slipped in an actual infinity when I said "forever". Perhaps
I should have said "indefinitely" ;)
Tom
--~--~-~--~~~---~--~--
Bruno Marchal wrote:
>
> OK. And you are right, I could have done this without mentioning the
> constructive ordinal. But it is worth mentioning it, even at this early
> stages, because they will reappear again and again.
> Note that all those infinite but constructive ordinal are all countable
>
Le 30-mai-06, à 03:14, Tom Caylor a écrit :
> OK. I see that so far (above) there's no problem. (See below for
> where I still have concern(s).) Here I was taking a fixed N, but G is
> defined as the diagonal, so my comparison is not valid, and so my proof
> that G is infinite for a fixed N
I meant that it makes intuitive sense that you *cannot* sequence
effectively on all computable growing functions.
Tom
--~--~-~--~~~---~--~~
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Bruno Marchal wrote:
> Le 26-mai-06, à 19:35, Tom Caylor a écrit :
> >
> > Bruno,
> > You are starting to perturb me! I guess that comes with the territory
> > where you're leading us.
>
> You should not worry too much. I confess I am putting your mind in the
> state of mathematicians before the
Le 26-mai-06, à 19:35, Tom Caylor a écrit :
>
> Bruno Marchal wrote:
>> Hi,
>>
>> OK, let us try to name the biggest natural (finite) number we can, and
>> let us do that transfinite ascension on the growing functions from N
>> to
>> N.
>>
>> We have already build some well defined sequence o
Bruno Marchal wrote:
> Hi,
>
> OK, let us try to name the biggest natural (finite) number we can, and
> let us do that transfinite ascension on the growing functions from N to
> N.
>
> We have already build some well defined sequence of description (code)
> of growing functions.
>
> Let us choose
Hi,
OK, let us try to name the biggest natural (finite) number we can, and
let us do that transfinite ascension on the growing functions from N to
N.
We have already build some well defined sequence of description (code)
of growing functions.
Let us choose the Hall Finney sequence to begin w
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