Another AC anomaly?
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From: WM on 27 Nov 2009 04:30 On 27 Nov., 08:41, Virgil <Vir...(a)home.esc> wrote: > In article > <aa9e46c0-56da-4510-8345-8dee84745...(a)b2g2000yqi.googlegroups.com>, > > > > > > WM <mueck...(a)rz.fh-augsburg.de> wrote: > > On 27 Nov., 02:50, William Hughes <wpihug...(a)hotmail.com> wrote: > > > On Nov 26, 4:51 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > > On 26 Nov., 19:22, William Hughes <wpihug...(a)hotmail.com> wrote: > > > > > Only in Wolkenmuekenheim. Outside of Wolkenmuekenheim > > > > > you will have an empty set. > > > > > Besides your assertion, you have arguments too, don't you? > > > > In particular you can explain, how the empty set will emerge while > > > > throughout the whole time the minimum contents of the vase is 1 ball? > > > > Since outside of Wolkenmuekenheim there is no reason to > > > expect the number of balls to be continuous at infinity > > > Why then do you expect the digits of Cantor's diagonal number to be > > "continuous" at infinity (contrary to being *not* at infinity)? > > Why would anyone ever expect a numerical digit to be continuous? > > All the ones I am aware of are members of a finite set of discrete > objects. And there is none that does not belong to a rational number. > > And why would you expect to find a digit of any sort "at infinity", when > there is no such a position as "at infinity". If there is no "at infinity", then there cannot be a "behind infinity", so there is no omega and no omega + 1. In fact you are right - as so often. There is no "at infinity". The vase is never empty. There is no smallest positive rational, There are not all rationals. Regards, WM
From: Alan Smaill on 27 Nov 2009 05:43 WM <mueckenh(a)rz.fh-augsburg.de> writes: > We are talking about a vase which is never emptied completely! > > Hence it cannot be empty unless "infinity" is identical to "never". > But this describes potential infinity and excludes phantasies like > Cantor's finished diagonal number. But you lose control at infinity! So your "hence" doesn't work. I have that on good authority. > Regards, WM > > Regards, WM -- Alan Smaill
From: William Hughes on 27 Nov 2009 08:48 On Nov 27, 2:45 am, WM <mueck...(a)rz.fh-augsburg.de> wrote: > On 27 Nov., 02:50, William Hughes <wpihug...(a)hotmail.com> wrote: > > > On Nov 26, 4:51 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > On 26 Nov., 19:22, William Hughes <wpihug...(a)hotmail.com> wrote: > > > > Only in Wolkenmuekenheim. Outside of Wolkenmuekenheim > > > > you will have an empty set. > > > > Besides your assertion, you have arguments too, don't you? > > > In particular you can explain, how the empty set will emerge while > > > throughout the whole time the minimum contents of the vase is 1 ball? > > > Since outside of Wolkenmuekenheim there is no reason to > > expect the number of balls to be continuous at infinity > <snip attempted change of subject> The argument why the change is the number of balls is not problem is simple. Outside Wolkenmuekenheim There is a contradiction at the last step There is no last step There is no contradiction. Of course inside Wolkenmuekenheim ANYTHING can change (lists, sets, last elements, fixed last elements etc.) There is a contradiction at the last step. There is a last step (it is something that changes) There is a contradiction. - William Hughes
From: WM on 27 Nov 2009 09:25 On 27 Nov., 11:43, Alan Smaill <sma...(a)SPAMinf.ed.ac.uk> wrote: > WM <mueck...(a)rz.fh-augsburg.de> writes: > > We are talking about a vase which is never emptied completely! > > > Hence it cannot be empty unless "infinity" is identical to "never". > > But this describes potential infinity and excludes phantasies like > > Cantor's finished diagonal number. > > But you lose control at infinity! > So does Cantor. > So your "hence" doesn't work. It works if there is anyone who does not lose control at infinity. That's enough. Regards, WM
From: WM on 27 Nov 2009 09:29
On 27 Nov., 14:48, William Hughes <wpihug...(a)hotmail.com> wrote: ********************* you will have an empty set. ******************** > > > > > Besides your assertion, you have arguments too, don't you? > > > > In particular you can explain, how the empty set will emerge while > > > > throughout the whole time the minimum contents of the vase is 1 ball? > > > > Since outside of Wolkenmuekenheim there is no reason to > > > expect the number of balls to be continuous ***************** at infinity ***************** > > The argument why the change is the number > of balls is not problem is simple. Outside Wolkenmuekenheim > > There is a contradiction at the last step > There is no last step > There is no contradiction. Therefore the vase is never empty - and the only error is your assertion it would be empty after the last step and there was a state of the vase "at infinity". Regards, WM |