halting problem proof, via diagonalization?
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From: Balthasar on 8 Aug 2008 19:35 On 8 Aug 2008 16:09:48 -0700, stevendaryl3016(a)yahoo.com (Daryl McCullough) wrote: > > No, the anti-diagonal does *not* equal the "limit entry". > It doesn't? So YOU know how the /limit entry/ is defined? Well, at least *I* don't know how it is defined, hence *I* can't claim that - since I don't have a proof for this assertion. [...] > > Why would you think that? > Because he's a troll or a crank? > > The differences *don't* tend to zero. > Well, here I have to disagree. Actually, they do - in a certain sense. (Of course: so what?!) I mean, with the construction of the anti-diagonal you ensure that the anti-diagonal differs from the n-th entry in the list _at least_ in the n-th digit. Hence this "guaranteed difference" tends to zero (as n tends to oo). But so what? We all (non-cranks that is) know that even though the difference between 1/n and 0 tends to zero (as n tends to oo), 0 still does not occur in the sequence (1/n). With other words: ~En e IN: 0 = 1/n. (@Crank: 0 is not an entry in the sequence (1/n).) 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: julio on 8 Aug 2008 19:39 On 9 Aug, 00:31, MoeBlee <jazzm...(a)hotmail.com> wrote: > On Aug 8, 4:23 pm, ju...(a)diegidio.name wrote: > > > > > > > On 9 Aug, 00:16, Balthasar <nomail(a)invalid> wrote: > > > > On Fri, 8 Aug 2008 15:49:27 -0700 (PDT), MoeBlee <jazzm...(a)hotmail.com> > > > wrote: > > > > > P.S. It is decidedly NOT constructivist to assert the existence of a > > > > "limit" without CONSTRUCTING it (and just saying "the limit case" is > > > > decidedly not a construction), let alone, not even defining what > > > > possible sense you might mean by a "limit" in such a context. > > > > And, btw., even a constructivist/intuitionist would agree that a number > > > is not in a certain set (or list) if it differs from ALL (i.e. each and > > > every) elements (or entries) in the set (or list). ;-) > > > Paralogism. As usual you are assuming what there is to prove, that's > > what anyone knowing about logic would say. And in my argument I do NOT > > even assume anything like that, I actually conclude the opposite. > > Clueless as you can be, can you be sooo clueless? > > Okay, go ahead and keep thinking that... I will. You have of course snippned it, but Balthasar had provided it in formulas. You lose, badly now. And I am officially the new "king of the post-cantorians", by your own appointment. Cooool. -LV > > MoeBlee
From: julio on 8 Aug 2008 19:41 On 9 Aug, 00:16, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > ju...(a)diegidio.name says... > > >So you cannot add anything significant, you just reiterate your > >insults to my intelligence. Never mind, it was anyway very > >"instructive". > > Look, Cantor made a precise claim, and he gave a rigorous proof > of that claim. You made a fuzzy claim (one that didn't actually > contradict what Cantor said), and you gave a false proof of that > fuzzy claim. I guess it's not nice to insult your intelligence, > but you clearly don't know what you are talking about. And you clearly can only reiterate you spell. Have fun. -LV > -- > Daryl McCullough > Ithaca, NY
From: MoeBlee on 8 Aug 2008 19:42 On Aug 8, 4:39 pm, ju...(a)diegidio.name wrote: > On 9 Aug, 00:31, MoeBlee <jazzm...(a)hotmail.com> wrote: > > On Aug 8, 4:23 pm, ju...(a)diegidio.name wrote: > > > > On 9 Aug, 00:16, Balthasar <nomail(a)invalid> wrote: > > > > > On Fri, 8 Aug 2008 15:49:27 -0700 (PDT), MoeBlee <jazzm...(a)hotmail.com> > > > > wrote: > > > > > > P.S. It is decidedly NOT constructivist to assert the existence of a > > > > > "limit" without CONSTRUCTING it (and just saying "the limit case" is > > > > > decidedly not a construction), let alone, not even defining what > > > > > possible sense you might mean by a "limit" in such a context. > > > > > And, btw., even a constructivist/intuitionist would agree that a number > > > > is not in a certain set (or list) if it differs from ALL (i.e. each and > > > > every) elements (or entries) in the set (or list). ;-) > > > > Paralogism. As usual you are assuming what there is to prove, that's > > > what anyone knowing about logic would say. And in my argument I do NOT > > > even assume anything like that, I actually conclude the opposite. > > > Clueless as you can be, can you be sooo clueless? > > > Okay, go ahead and keep thinking that... > > I will. > > You have of course snippned it, but Balthasar had provided it in > formulas. I have no idea what you think I snipped in my last post. > You lose, badly now. > > And I am officially the new "king of the post-cantorians", by your own > appointment. > > Cooool. Sweet indeed. MoeBlee
From: Balthasar on 8 Aug 2008 19:46
On Fri, 8 Aug 2008 16:29:38 -0700 (PDT), MoeBlee <jazzmobe(a)hotmail.com> wrote: >> >> Balthasar is now your friend. And I am finished with you both. >> Oh, how sad! :-( I'm deeply hurt! 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) |