A BLATENT FLAW in Cantor's diag proof
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From: George Greene on 10 Jun 2010 00:41 On Jun 9, 8:06 am, William Hughes <wpihug...(a)hotmail.com> wrote: > Nope. E.g. there is no way to order > the list of all computable numbers > to make it a computable list. There is a natural order among the TMs doing the computing, THEMselves. But I am now guessing that telling whether a TM computes a computable number OR NOT is analogous to telling whether it halts. Turing himself IIRC had a different convention for what it meant for a TM to represent a number in any case.
From: Tim Little on 10 Jun 2010 00:48 On 2010-06-10, |-|ercules <radgray123(a)yahoo.com> wrote: > If the diag argument doesn't work on a hypothetical list it doesn't > work at all. It works on any list of infinite sequences. > The hypothetical list of all computable reals is a subset of my > list. You haven't yet given any consistent definition for "your" list. Not that it matters, since the diagonal argument will work on it anyway. > If no new sequence can be found that is not on a subset of my list, You can stop there, since a new sequence can be found. - Tim
From: George Greene on 10 Jun 2010 00:53 On Jun 10, 12:48 am, Tim Little <t...(a)little-possums.net> wrote: > On 2010-06-10, |-|ercules <radgray...(a)yahoo.com> wrote: > > > If the diag argument doesn't work on a hypothetical list it doesn't > > work at all. > > It works on any list of infinite sequences. It works on any SQUARE list. I.e. any vertical list of horizontal lists, with the same number of rows as columns. It may or may not work on lists with a fixed number of columns and a GREATER number of rows; If you have 3 columns and 4 rows then it is possible that the 4th row is the anti-diag of the first 3. On lists with more columns than rows, it arguably cannot apply at all since the width of the list you get from trying to diagonalize IS TOO SHORT to be another row.
From: George Greene on 10 Jun 2010 00:56 On Jun 8, 11:50 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Yet there is no shortage of people strangely willing to give it a try. There is a shortage of people qualified to try. Half the people who are trying (this is even truer in the case of WM) understand the whole situation less well than Herc. Herc, unfortunately, though, is not serious about understanding anything. He thinks he actually knows something already.
From: George Greene on 11 Jun 2010 17:58
On Jun 9, 5:17 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > You seem firm in your beliefs, and the meaning of the post is lost on you yet again. Do we need to coin a new category of irony for this? Solipsistic irony? A purer example has rarely been seen; though he doesn't know it, this is Herc that Herc is talking about. |