Why can no one in sci.math understand my simple point?
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From: WM on 22 Jun 2010 07:28 On 22 Jun., 11:49, Sylvia Else <syl...(a)not.here.invalid> wrote: > The antidiagonal of the list of (A0, A1, A2,...) would only belong to > the set if it is also the antidiagnoal of some Ln, which you haven't > proved to be the case. Ah, noew I understand. You want to make us believe that there is a limiting list but no limiting antidiagonal. The list containing (L0, A0, A1, A2,...) would only then be a list Ln, if its antidiagonal is the antidiagonal of some Ln. But if (L0, A0, A1, A2,...) is not a list Ln, then something must have been happened in between that was incompatible with the process of my proof. Regards, WM
From: Sylvia Else on 22 Jun 2010 08:34 On 22/06/2010 9:28 PM, WM wrote: > On 22 Jun., 11:49, Sylvia Else<syl...(a)not.here.invalid> wrote: > > >> The antidiagonal of the list of (A0, A1, A2,...) would only belong to >> the set if it is also the antidiagnoal of some Ln, which you haven't >> proved to be the case. > > Ah, noew I understand. You want to make us believe that there is a > limiting list but no limiting antidiagonal. Hadn't even crossed my mind. > > The list containing (L0, A0, A1, A2,...) would only then be a list Ln, > if its antidiagonal is the antidiagonal of some Ln. > > But if (L0, A0, A1, A2,...) is not a list Ln, then something must have > been happened in between that was incompatible with the process of my > proof. > Strictly speaking, by your method of construction, the lists are (L0), (A0, L0), (A1, A0, L0), (... , A2, A1, A0, L0) ... being respectively, L0, L1, L2, L3, ... For (A0, A1, A2, ...) to be a list that should contain its own anti-diagonal, it has to be the same as an Ln, yet I can see no reason to think it would be. The fact that a contradiction would arise seems a powerful indicator that (A0, A1, A2, ...) would not be same as any Ln. Sylvia.
From: Newberry on 22 Jun 2010 11:29 On Jun 21, 9:38 pm, Virgil <Vir...(a)home.esc> wrote: > In article > <2896ff83-7d48-4bcb-80fa-ea38b8e1b...(a)40g2000pry.googlegroups.com>, > > > > > > Newberry <newberr...(a)gmail.com> wrote: > > On Jun 21, 6:11 am, Sylvia Else <syl...(a)not.here.invalid> wrote: > > > On 21/06/2010 1:39 PM, Newberry wrote: > > > > > Not sure why you think you had to tell us how the anti-diagonal is > > > > defined. You claimed you could CONSTRUCT it. Please go ahead and do > > > > so. > > > > I'm sure he will - right after you provide the list of reals. > > > > Sylvia. > > > Dear Sylvia, I did not claim that I could construct a list of reals, > > but Virgil claimed he could construct an anti-diagonal. > > To what list? > > An antidiagonal to a list of decimal representations of reals is simple. > > Ignore any integer digits (to the left of the decimal point) in the > listed numbers and have 0 to the left of the decimal point in the > anti-diagonal. If the nth decimal digit of the nth listed number is 5, > then make the nth decimal digit of the antidiagonal 7, otherwise make it > 3. > > This rule prevents it from being equal to any real in the listing. > > The above is only one of many effective rules for constructing an > antidiagonal different from each listed number. How is this effective if the diagonal has infinite amount of information? > If, as in Cantor's original argument, one has a list of binary > sequences, one takes the nth value of the antidiagonal to be the > opposite value from the nth value of the nth listed sequence.- Hide quoted text - > > - Show quoted text -
From: David R Tribble on 22 Jun 2010 11:49 WM wrote: > A crank suffers from selective perception of reality, doesn't he? Why yes, he does.
From: Mike Terry on 22 Jun 2010 12:27
"WM" <mueckenh(a)rz.fh-augsburg.de> wrote in message news:b71db24f-d637-4afd-a717-d2b5055f4fbf(a)a30g2000yqn.googlegroups.com... > On 22 Jun., 11:49, Sylvia Else <syl...(a)not.here.invalid> wrote: > > > > The antidiagonal of the list of (A0, A1, A2,...) would only belong to > > the set if it is also the antidiagnoal of some Ln, which you haven't > > proved to be the case. > > Ah, noew I understand. You want to make us believe that there is a > limiting list but no limiting antidiagonal. > > The list containing (L0, A0, A1, A2,...) would only then be a list Ln, > if its antidiagonal is the antidiagonal of some Ln. L0 is not a number. It's a list, and so is not eligible for belonging to a list of numbers. (I.e. this response makes no sense.) ----------------- So this is where I believe this sub-thread has got to as of Tue 16:00 UTC: (to stop us going round and around) WM has defined a sequence of lists (L0, L1, ...) with corresponding antidiags (A0, A1, ...). There is a claim that "the set of antidiagonals" appears to be uncountable, but it was not clear which set this was. WM seemed to suggest he meant the set (A0, A1, ...). I pointed out this was obviously countable. WM agreed but said it can't be written as a list, since it's antidiag is in the list. Sylvia pointed out why this is obviously wrong. WM has now suggested an alternative list (L0, A0, A1,...) but that is not a valid list of numbers. It is true none the less that the image of L0 is countable, and if we append all the A0, A1,... it is still countable, so the combined set IS listable. Suppose LW lists this new set. Of course LW has a NEW antidiagonal which is not in the list LW, so this isn't going anywhere. So that's where we are currently I think. Regards, Mike. |