Cantor Confusion
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From: Virgil on 16 Oct 2006 15:40 In article <1161004988.055723.235170(a)e3g2000cwe.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > > According to the ZFC system: The vase is empty at noon, because all > > > natural numbers left it before noon. > > > By means of the ZFC system we can formulate sequences and their limits > > > in mathematical language. From this it follows that lim {n-->oo} n > 1. > > > And from this it follows that the vase is not empty at noon. > > > > By what axiom do you conclude that the limit as t increases towards noon > > of any function and the value of that function at noon must be the same? > > By that or those axiom(s) which lead(s) to the result lim {t-->oo} 1/t > = 0. Then "Mueckenh"must be claiming that 1/t is continuous at t = 0, as that would be the only justification for saying that the value of 1/t at 0 equals the limit at t goes to zero. And any such a claim of continuitiy of 1/t at t = 0 displays "Mueckenh"'s incompetence.
From: mueckenh on 16 Oct 2006 15:41 Alan Morgan schrieb: > In article <1160944143.122919.243860(a)h48g2000cwc.googlegroups.com>, > <mueckenh(a)rz.fh-augsburg.de> wrote: > > > >William Hughes schrieb: > > > >> However, you wish to do more. You want to show > >> that claiming "N does not have an upper bound and > >> N exists as a complete set" leads to a contradiction.] > >> > >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. > > Agreed. Do you know what "for all n e N" means? There are *not any* further natural numbers. There is no chance to increase the cardinal number. > > >There is no larger natural number than aleph_0 = |{2,4,6,...}|. > >Contradiction, because there are only natural numbers in {2,4,6,...}. > > That would be a contradiction only if Aleph0 e N, but it isn't. Your > statement above is true for finite n. Showing that it isn't true for > infinite n (or in the limit or whatever terminology you choose to use) > does not produce a contradiction. There are no infinite n, whatever terminology you coose. And aleph_0 is considered larger than any finite n. That is simply impossible. There must be finite even numbers X, larger than 2n, which complete the set {2,4,6,..., 2n, X }. They push the cardinality but do not increase the sizes of numbers. Regards, WM
From: David Marcus on 16 Oct 2006 15:43 Han de Bruijn wrote: > David Marcus wrote: > > > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > > >>David Marcus schreef: > >> > >>>Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>> > >>>>David Marcus schreef: > >>>> > >>>>>Han de Bruijn wrote: > >>>>> > >>>>>>I'm not interested in the question whether set theory is mathematically > >>>>>>inconsistent. What bothers me is whether it is _physically_ inconsistent > >>>>>>and I think - worse: I know - that it is. > >>>>> > >>>>>What does "physically inconsistent" mean? Wouldn't your comments be > >>>>>better posted to sci.physics? Most people in sci.math are (or at least > >>>>>think they are) discussing mathematics. > >>>> > >>>>ONE world or NO world. > >>> > >>>Sorry. No idea what you mean. Do you have anything to say about > >>>mathematics or would you prefer we all just ignore you? > >> > >>It would save me a lot of time if some people here start to ignore me. > > > > Does that mean you have nothing to say about mathematics? > > Sigh! Start digging into my website. I've said more about mathematics > than anybody else in 'sci.math'. I'm sorry, but I looked at your website and couldn't find anything about Mathematics. If you do have something to say, please say it here and say it concisely. -- David Marcus
From: Han.deBruijn on 16 Oct 2006 15:43 MoeBlee schreef: > Han de Bruijn wrote: > > Sigh! Start digging into my website. I've said more about mathematics > > than anybody else in 'sci.math'. > > That's hilarious! I didn't even have dig at all to find you proposing > an inconsistent set of axioms and blaming not yourself but set theory > for the inconsistency - on the very first page I saw at that web site! Dig deeper! Han de Bruijn
From: mueckenh on 16 Oct 2006 15:43
Dik T. Winter schrieb: > In article <1160933229.072292.316580(a)e3g2000cwe.googlegroups.com> Han.deBruijn(a)DTO.TUDelft.NL writes: > > Dik T. Winter schreef: > > > In article <1160856895.115824.134080(a)b28g2000cwb.googlegroups.com> > > > Han.deBruijn(a)DTO.TUDelft.NL writes: > ... > > > > Come on, guys! You all know that, in the world of approximations, > > > > 2 _is_ the square of a rational and the circle _is_ squared. > > > > > > I thought you were talking mathematics? > > > > I thought approximations were a part of mathematics? > > They are. Numerical mathematics in particular. But also in them, 2 is > *not* the square of a rational number. The best you can state is that > there is a rational number whose square approximates 2 with a certain > precision. Correct. Doing better is impossible. Regards, WM |