Cantor Confusion
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From: Virgil on 18 Oct 2006 15:43 In article <59aa8$4535e9b9$82a1e228$30545(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <e82a9$4535d64e$82a1e228$22073(a)news1.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > >>Virgil wrote: > >> > >>>In article <7d12f$4534cca1$82a1e228$21528(a)news1.tudelft.nl>, > >>> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>> > >>>>Virgil wrote: > >>>> > >>>>>In article <1161029391.305685.141910(a)b28g2000cwb.googlegroups.com>, > >>>>>Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>>>> > >>>>>>Sure, theories. Can't you talk about something else but "theories"? > >>>>> > >>>>>Isn't the point of physics to come up with theories? > >>>> > >>>>AND experiments. All physical theories are judged by experiments. > >>>> > >>>>>And now a physicist wants to outen them? > >>> > >>>Does HdB suggest that there are no standards by which to judge mental > >>>theories? > >> > >>No. But these standards are not mental. > > > > How does HdB apply his Jo Blocks to mental theories? > > Huh? What are Jo Blocks? > > Han de Bruijn Physicists, particularly those of HdB's philosophical idiosyncrasies, should know about them.
From: mueckenh on 18 Oct 2006 15:45 Virgil schrieb: > In article <1161079685.233073.120000(a)k70g2000cwa.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: > > > MoeBlee schrieb: > > > > There is no "equal weight" in the proof. > > > > > > > You haven't yet noticed it? Each digit of the infinitely many digits of > > the diagonal number has the same weight or importance for the proof. > > It is only necessary that each digit have non-zero weight in order for > the difference between the diagonal and one of the list to be non-zero. > > > > In > > mathematics, the weight of the digits of reals is 10^(-n). > At least in decimal notation, but as that makes all the weights > non-zero, that is sufficient to distinguish the diagonal from each of > the listed numbers. Only for a finite diagonal. In the infinite case we have for example 1 = 0.999... > > >Infinite > > sequences of digits with equal weight are undefined and devoid of > > meaning. > > As no such sequences are involved, the comment is irrelevant. The diagonal is not an infinite sequence? Regards, WM
From: mueckenh on 18 Oct 2006 15:46 Virgil schrieb: > In article <1161103769.338793.195850(a)i42g2000cwa.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: > > > William Hughes schrieb: > > > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > William Hughes schrieb: > > > > > > > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > > William Hughes schrieb: > > > > > > > > > > > > > > But the end time of the problem (noon) does not correspond to > > > > > > > an integer (neither in standard mathematics, nor in your > > > > > > > system, whether or not you interpret the problem as dealing > > > > > > > with infinite integers as well as finite integers). So the > > > > > > > function > > > > > > > 9n does not have a value at noon. There is no way > > > > > > > it can be continuous at noon. And since there is no > > > > > > > value of n that corresponds to noon, 9n cannot be used > > > > > > > to determine the number of balls in the vase at noon. > > > > > > > > > > > > But the function n can be used to determine the number of balls > > > > > > removed > > > > > > from the vase at noon? > > > > > > > > > > > > > > > > Nope. [There are no balls removed from the vase at noon] > > > > > > > > Arbitrary misunderstanding? > > > > > > > > > The function 9n has nothing to do with the number of > > > > > balls in the vase at noon. > > > > > > > > But the function n can be used to determine the number of balls having > > > > been removed > > > > from the vase at noon? > > > > > > > > > No. There are no balls removed from the vase at noon. > > > > > > Note, that there is no time "just before noon". At any time > > > before noon there remain an infinite number of steps. > > > > > > So no value of n is close to the end. > > > > > > The balls are removed during an infinite number of > > > steps. > > > > Please read carefully: But the function n can be used to determine the > > number of balls *having been* removed from the vase at noon? (That > > means up to noon.) > > Yes. All of them are. So you act and think biased. That is not science and not mathematics. Regards, WM
From: Virgil on 18 Oct 2006 15:48 In article <1161182168.538010.12650(a)f16g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > N = omega = aleph 0. How should one of them have different character? > According to Cantor, set theory deals with actual infinity, not with > potential. Cantor died in 1918. Things have progressed a bit since then.
From: mueckenh on 18 Oct 2006 15:51
David Marcus schrieb: > Han de Bruijn wrote: > > David Marcus wrote: > > > cbrown(a)cbrownsystems.com wrote: > > >>Han.deBruijn(a)DTO.TUDelft.NL wrote: > > >> > > >>>I talked about the real world, physics as an empirical science, > > >>>not about artifical theoretical constructs. In the real world, > > >>>Schrodinger's cat is dead :-( > > >> > > >>I thought you kept up with physics? > > >> > > >>http://physicsweb.org/articles/news/4/7/2 > > >> > > >>The device is conducting electricity in a clockwise fashion; and the > > >>device is not conducting electricity in a clockwise fashion. > > > > > > That interpretation of the experiment is probably dependent on theory. > > > Try this: > > > > > > http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/bmstartE.htm > > > > David Marcus is an adherent of some rather outdated Quantum Mechanical > > theories, as have been proposed in the middle of the past century, by > > David Bohm. Especially Bohm's theory of "hidden variables", which have > > never been found. (And IMO will never be found) > > Since the "hidden variables" are the positions of the particles, I think > we find them all the time. Kind of bizarre to call a particle's position > a "hidden variable". Nice to see you are just as illogical in your > beliefs about physics as about mathematics. Hidden variables do exist in exactly the same manner as the well-order of the reals. Waves have no fixed positions or velocities. I developed a theory describing hidden variables obeying the Bell inequalities (A Review of Extended Probabilities, Phys. Rep. 133 (1986) 337). Alas, it turned out that negative probabilities were required. Regards, WM |