Another AC anomaly?
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From: Virgil on 27 Nov 2009 14:38 In article <a02569c0-3b73-4c60-99f3-fbb1e9d28391(a)b15g2000yqd.googlegroups.com>, WM <mueckenh(a)rz.fh-augsburg.de> wrote: > On 27 Nov., 18:50, William Hughes <wpihug...(a)hotmail.com> wrote: > > On Nov 27, 1:32�pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > > So all steps have been done whereas the last is pending. > > > > Nope. �Outside of Wolkenmeukenheim > > we can do all steps without doing a last step �So all steps > > have been done, �however there is no last step so the last > > is not pending. > > Whatever you may think. If you wish to argue that the sequence of > balls has limt 0 then you are outside of mathematics. And there is no > need to further answer your "arguments". Since Mueckenheim so seldom manages to get himself inside of mathematics, he is hardly an authority on what goes on there. N mathematics, it is quite possible, even common, for an infinite sequence to be completed and have a limit which is not a member of the sequence itself. And if the problem of the balls and urn can be stated unambiguously, and it has been, then its analysis can be done inside of mathematics, even though it does not appear to be possible in Wolkenmeukenheim.
From: William Hughes on 27 Nov 2009 14:39 On Nov 27, 3:23 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > On 27 Nov., 18:50, William Hughes <wpihug...(a)hotmail.com> wrote: > > > On Nov 27, 1:32 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > So all steps have been done whereas the last is pending. > > > Nope. Outside of Wolkenmeukenheim > > we can do all steps without doing a last step So all steps > > have been done, however there is no last step so the last > > is not pending. > > Whatever you may think <snip unsupported assertion> An unsupported assertion by WM will work in Wolkenmuekenheim, but is of no use outside Wolkenmeukenheim. - William Hughes
From: William Hughes on 27 Nov 2009 15:17 On Nov 27, 3:33 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > With only potential, i.e., not finished infinity, i.e., reasonable > infinity, the diagonal number (exchanging 0 by 1) of the following > list can be found in the list as an entry: > > 0.0 > 0.1 > 0.11 > 0.111 > ... Only in Wolkenmuekenheim where the argument goes Every entry in the list has a fixed last 1 The diagonal number does not have a fixed last 1 The diagonal number is an entry in the list - William Hughes
From: WM on 27 Nov 2009 16:24 On 27 Nov., 21:17, William Hughes <wpihug...(a)hotmail.com> wrote: > On Nov 27, 3:33 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > With only potential, i.e., not finished infinity, i.e., reasonable > > infinity, the diagonal number (exchanging 0 by 1) of the following > > list can be found in the list as an entry: > > > 0.0 > > 0.1 > > 0.11 > > 0.111 > > ... > > Only in Wolkenmuekenheim where the argument goes > > Every entry in the list has a fixed last 1 > The diagonal number does not have a fixed last 1 There is not a fixed last entry. > [...] Every diagonal number is in the list. Regards, WM
From: William Hughes on 27 Nov 2009 16:42
On Nov 27, 5:24 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > On 27 Nov., 21:17, William Hughes <wpihug...(a)hotmail.com> wrote: > > > On Nov 27, 3:33 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > With only potential, i.e., not finished infinity, i.e., reasonable > > > infinity, the diagonal number (exchanging 0 by 1) of the following > > > list can be found in the list as an entry: > > > > 0.0 > > > 0.1 > > > 0.11 > > > 0.111 > > > ... > > > Only in Wolkenmuekenheim where the argument goes > > > Every entry in the list has a fixed last 1 > > The diagonal number does not have a fixed last 1 > > There is not a fixed last entry So, every entry in the list has a fixed last 1. (We don't need a fixed last entry to say this) We still have Every entry in the list has a fixed last 1 The diagonal number does not have a fixed last 1 > Every diagonal number is in the list. Only in Wolkenmuekenheim. Outside of Wolkenmuekenheim there is only one diagonal number and it is not in the list. - William Hughes |