Cantor Confusion
in [Math]
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From: William Hughes on 1 Mar 2007 13:53 On Mar 1, 1:41 pm, mueck...(a)rz.fh-augsburg.de wrote: > On 1 Mrz., 01:48, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > > and being different from a collection of other sets it is *not* necessary > > that there is a single element where it differs from all those other sets. > > But this is necessary for linear sets, i.e, such sets which obey A1 c > A2 c A3 c ... > No. The set of all even naturals and its intitial segments give a counterexample. - William Hughes
From: Virgil on 1 Mar 2007 15:10 In article <1172740041.611220.208880(a)8g2000cwh.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > On 1 Mrz., 01:22, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > In article <1172650983.733643.316...(a)m58g2000cwm.googlegroups.com> > > mueck...(a)rz.fh-augsburg.de writes: > > > > > > > What is misleading about it if every mathmatician calls them "numbers"? > > It veils the physical restrictions. As numbers are not physical, they have no physical restrictions. > > > > sqrt(2) is in trichotomy with the rational numbers. > > In fact not even all rational numbers are numbers. You know, there are > less than 10^100 bits ... There is no theoretical limit, only practical ones, but mathematics is not limited by such practical considerations as it is purely theoretical. > > > So in your mathematical courses you call what we call the "complex > > numbers", > > "complex ideas" or something like that? > > I use the current words. I do not talk about these things there. So that anything that does not fit neatly into WM's theories, like complex numbers not having trichotomy, he chooses not to talk about.
From: mueckenh on 1 Mar 2007 15:36 On 1 Mrz., 11:45, Franziska Neugebauer <Franziska- Neugeba...(a)neugeb.dnsalias.net> wrote: > mueck...(a)rz.fh-augsburg.de wrote: > > On 1 Mrz., 01:22, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > >> In article <1172650983.733643.316...(a)m58g2000cwm.googlegroups.com> > >> mueck...(a)rz.fh-augsburg.de writes: > > >> What is misleading about it if every mathmatician calls them > >> "numbers"? > > > It veils the physical restrictions. > > There is no objective in mathematics to "unv[e]il" physical (material) > restrictions of the world. After having recognized them there is the necessity to investigate them because they cannot be avoided - at most they can be displaced. But displacement promotes neurosis. I prefer scientific truth. Regards, WM
From: Franziska Neugebauer on 1 Mar 2007 16:59 mueckenh(a)rz.fh-augsburg.de wrote: > On 1 Mrz., 11:45, Franziska Neugebauer <Franziska- > Neugeba...(a)neugeb.dnsalias.net> wrote: >> mueck...(a)rz.fh-augsburg.de wrote: >> > On 1 Mrz., 01:22, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: >> >> In article <1172650983.733643.316...(a)m58g2000cwm.googlegroups.com> >> >> mueck...(a)rz.fh-augsburg.de writes: >> >> >> What is misleading about it if every mathmatician calls them >> >> "numbers"? >> >> > It veils the physical restrictions. >> >> There is no objective in mathematics to "unv[e]il" physical >> (material) restrictions of the world. > > After having recognized them Mission not yet accomplished. Please keep posting on until _we_ have "recognized them". Nonetheless I strongly urge you to contact IMU or AMS in order to register the new discipline. I suggest the name "restricted mathematics". F. N. -- xyz
From: David R Tribble on 1 Mar 2007 19:04
Han de Bruijn wrote: >> Do you deny that Mathematics is supposed to be a no-nonsense discipline? > Randy Poe wrote: > Lewis Carroll, a mathematician, was fond of playing > these semantic games but that doesn't make it mathematics. > > 1. Tyrannical governments are arbitrary. > 2. Let A be an any arbitrary government. > 3. Then A is tyrannical. Then there is: 1. Caterpillars eat cabbage. 2. Han eats cabbage. 3. Therefore Han is a caterpillar. |