Cantor Confusion
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From: Han de Bruijn on 18 Oct 2006 03:21 Virgil wrote: > In article <78269$4534cb2a$82a1e228$21528(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>_part_ of the question: do INFINITIES exist or not. Are they true or are >>they false? And IMO _that_ can be decided _now_, without rocket science. > > Do physical infinities exist? Probably not. Right! > Do physical triangles exist? Almost certainly not. Wrong! > Therefore, according to HdB's thesis, we should abolish trigonometry. The difference between (actual) infinities and (idealized) triangles is that the former can NOT be coarsened to something in physics that can be measured eventually, while the latter CAN be coarsened to something in physics that IS measurable. Han de Bruijn
From: Han de Bruijn on 18 Oct 2006 03:22 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. Han de Bruijn
From: Virgil on 18 Oct 2006 03:41 In article <a745$4535d5f4$82a1e228$22073(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <78269$4534cb2a$82a1e228$21528(a)news1.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > >>_part_ of the question: do INFINITIES exist or not. Are they true or are > >>they false? And IMO _that_ can be decided _now_, without rocket science. > > > > Do physical infinities exist? Probably not. > > Right! > > > Do physical triangles exist? Almost certainly not. > > Wrong! > > > Therefore, according to HdB's thesis, we should abolish trigonometry. > > The difference between (actual) infinities and (idealized) triangles is > that the former can NOT be coarsened to something in physics that can be > measured eventually, while the latter CAN be coarsened to something in > physics that IS measurable. > > Han de Bruijn The idealized infiniteness of ideal triangle sizes are coarsened to the finitely many things in physics that can be measured.
From: Virgil on 18 Oct 2006 03:43 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?
From: mueckenh on 18 Oct 2006 03:54
William Hughes schrieb: > In theory every possible way of describing a number is known > (this includes descrbing the representation). > I am afraid, here you are in error. Proof: If you were right, then also every impossible way of doing mathematics should be known. That implies that set theory should be known as inconsistent. Most of your party don't know that yet. > > > > Ingenuity may or may not be limited, but there is a limited amount > > > of time to communicate the results of ingenuity. > > > > Yes. It can be communicated, however, in highly compressed form. Also > > the compression depends on ingenuity. > > There are only a limited number of messages that can be communicated > during the lifetime of the universe. This incudes descriptions > and use of compression methods. But all you argue does not limit the size of a number. > > > > > > > > > > > > > > > > > > That is true too. And it is easy to see: If we define Lim [n-->oo] > > > > {1,2,3,...,n} = N, then we can see it easily: > > > > > > > > For all n e N we have {2,4,6,...,2n} contains larger natural numbers > > > > than |{2,4,6,...,2n}| = n. > > > > > > So we have something that is true for finite sets. > > > > It is true for finite numbers and sets of finite numbers. Should it not > > be true for all sequences of finite even numbers, then there must be > > some of even finite numbers, X, in {2,4,6,...,2n, X} which care to push > > the cardinality without increasing the sizes. That is obviously > > impossible. > > Nope. Adding a single element, or a finite > number of elements cannot take you > from a finite set to an infinite set. > You have to add an infinite number of elements. > So your set X above must be infinite. Adding an > infinite set to a finite set certainly changes the cardinality. Of course, but necessarily it also changes the maximum sizes of elements. As long as the sizes all are finite, the cardinality is finite too. You assume that only the one is changed, the other is not. But you seem not to be aware that in natural numbers size and cardinality are strictly the same while with the even natural numbers size grows faster than cardinality. Therefore, for every set X we have again the same problem but in increased form: X contains by far larger elements than expressed by its cardinality (because the smaller ones are already used up). > > > > > > > > There is no larger natural number than aleph_0 = |{2,4,6,...}|. > > > > Contradiction, because there are only natural numbers in {2,4,6,...}. > > > > > Wiithout any justification whatsoever you state something > > > about infinite sets. > > > > I state something about finite numbers. > > You state something about the set {2,4,6,...} That are finite numbers. > > > > > > > Something that is true about finite sets does not have to > > > be true about infinite sets. > > > > That is your standard excuse. It seems that nothing can be true for > > infinite sets. > > Piffle. If I were to say "Something that is true about sets of > integers > does not have to be true about sets of real numbers" would > you say "It seems that nothing can be true for sets of real numbers"? That is a wrong example. The set N consists o finite numbers. If it contained infinite numbers, you could be right, but that were uninteresting. > > > > The brain is contstrained by physical laws. The concepts produced by > > > the brain are not contrained by physical laws. > > > > The puppet hangs on the string. The feet of the puppet hang on the > > puppet, but not on the string? They do not fall down when the string is > > cut? > > The beauty of the puppet cannot exist without the puppet. If the > string > is cut the beauty of the puppet does not fall down. If the puppet falls down and if it is of porcelain, the beauty is gone. Regards, WM |