halting problem proof, via diagonalization?
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From: julio on 8 Aug 2008 13:23 On 8 Aug, 18:12, Balthasar <nomail(a)invalid> wrote: > On Fri, 8 Aug 2008 09:44:09 -0700 (PDT), MoeBlee <jazzm...(a)hotmail.com> > wrote: > > >> Below again a simple argument to show that from the very same > >> construction we could induce the exact opposite result: > > >> 1: The diagonal differs from the 1st entry in the 1st place; > >> 2: The diagonal differs from the 2nd entry in the 2nd place; > >> ... > >> n: The diagonal differs from the n-th entry in the n-th place; > > >> It seems straightforward to induce that, at the limit, the difference > >> between the diagonal and the limit entry tends to zero. > > > WHAT limit? You need to DEFINE "limit" in terms of some topology, > > metric, ordering, or whatever. We don't just use the word "limit" > > without the context of the EXACT sense of a limit as it has been > > DEFINED. > > > Moreover, the anti-diagonal differes from every entry in the list. > > That's all that is required to show that the anti-diagonal is not on > > the list. > > To make a long story short: we are not interested in the "limit entry" > (whatever that may be), but in the fact that the diagonal differs from > each and any entry in the list. Interested or not, you cannot just dismiss it. The "limit" entry makes just as much sense as the above (or the below) "[for] every entry in the list". Is the list "infinite" or is it not? I am saying, yours is not a valid objection. -LV > Of course there's still a loophole mentioned by WM, see signature below. > > B. > > -- > > "For every line of Cantor's list it is true that this line does not > contain the diagonal number. Nevertheless the diagonal number may > be in the infinite list." (WM, sci.logic)
From: MoeBlee on 8 Aug 2008 14:03 On Aug 8, 10:03 am, ju...(a)diegidio.name wrote: > On 8 Aug, 17:53, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > > ju...(a)diegidio.name writes: > > > The "limit" is of course induction. > > > Alas, that makes no sense whatsoever. > > Doesn't it? No, it doesn't. It's been explained to you over and over (and then you complain about repetition), but it's clear by now that you just don't want to understand the mathematical explanations as it suits you better to posture. MoeBlee
From: Balthasar on 8 Aug 2008 14:08 On Fri, 8 Aug 2008 11:03:55 -0700 (PDT), MoeBlee <jazzmobe(a)hotmail.com> wrote: > > ... but it's clear by now that you just don't want to understand the > mathematical explanations as it suits you better to posture. > Sure? I'd suppose to try harder, Moe! Don't give up so fast! :-) B. -- "For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list." (WM, sci.logic)
From: MoeBlee on 8 Aug 2008 14:10 On Aug 8, 10:23 am, ju...(a)diegidio.name wrote: > > To make a long story short: we are not interested in the "limit entry" > > (whatever that may be), but in the fact that the diagonal differs from > > each and any entry in the list. > > Interested or not, you cannot just dismiss it. The "limit" entry makes > just as much sense as the above (or the below) "[for] every entry in > the list". Is the list "infinite" or is it not? I am saying, yours is > not a valid objection. Whether the list is infinite or NOT, the anti-diagonal is not on the list. Otherwise, you are free to mention EXACTLY what premises in the proof or what rule of logic used you disagree with. Then we could at least say, "Yes, given that you don't accept those premises and rules of logic, you don't have to accept the theorem that is proved from them. Now, what premises and logic DO you accept for the purpose of deriving mathematical conclusions?" See, that would be productive. But we can't get there if all you do is use UNDEFINED hocus pocus about "limit induction", and amphiboly in your symbolisms, along with recriminations about what dishonest idiots mathematicians are. MoeBlee
From: Balthasar on 8 Aug 2008 14:18
On Fri, 8 Aug 2008 11:10:36 -0700 (PDT), MoeBlee <jazzmobe(a)hotmail.com> wrote: >>> >>> To make a long story short: we are not interested in the "limit entry" >>> (whatever that may be), but in the fact that the diagonal differs from >>> each and any entry in the list. >>> >> Interested or not, you cannot just dismiss it. [Crank] >> Well, actually there's nothing to "dismiss". B. -- "For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list." (WM, sci.logic) |