Cantor Confusion
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From: Dik T. Winter on 31 Oct 2006 10:13 In article <1162301684.964597.250790(a)f16g2000cwb.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: > Dik T. Winter schrieb: > > In article <1162157341.348431.26550(a)h48g2000cwc.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: .... > > > > The Algebraic Eigenvalue Problem, by J. H. Wilkinson. But of > > > > course you know that book because, almost certainly, you use > > > > methods for calculations that are based on the methodology > > > > developed in that book. > > > > No comments on this, Wolfgang? > > No, Dik, I did not read hat book. I use only trivial classical > mathematics like Algebra, Anaylsis, number theory. You do not use numerical mathematics during your physics research? But whatever, did you read Hardy and Wright? > > > Do and enjoy your mathematics. I will not disturb you. I am not very > > > familiar with those things, but they may be very valuable. > > > > In that case, why are you stating again and again that my mathematics is > > wrong? > > The foundations are wrong. There is no uncountable set. For some > arguments look here: > http://www.fh-augsburg.de/~mueckenh/MR/Argumente.mht Sorry, that is not a valid HTML document and will not display properly. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Dik T. Winter on 31 Oct 2006 10:26 In article <1162302240.954226.285750(a)f16g2000cwb.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: > Dik T. Winter schrieb: > > In article <1162157584.352015.276510(a)e3g2000cwe.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: .... > > > Because I can construct parallels (or see their absence) but I cannot > > > see a well-order which is not definable. > > > > Indeed, what you do not see does not exist, and when others see it they > > are talking nonsense. How more opinionated you can get? > > Everybody knows that a well order of the reals is not definable. Please > let me know how the well order should be realized, because the prove of > existence means that it can be realized. An existence proof does *not* show that it is realisable. But, please be aware, that that existence proof is *only* possible with an additional axiom: the axiom of choice. And indeed, there is an easy existence proof of a countable list of computable numbers, and there is also a proof that that countable list is not computable (so not realisable). > > Oh, well, just in another thread there is a discussion about the existence > > proof and showing a method to calculate such a thing. An existence proof > > does not necessarily imply a method to actually provide such a thing. > > There is a mathematical proof that li(x) - pi(x) changes sign infinitely > > often. In your finite world you will never see such a sign change. > > In my world it is not excluded, to my knowledge, to find as many sign > changes as desired. I think it is excluded in your finitistic world. And, I think, that indeed the universe is not able to provide the computer power to actually observe such a sign change. To do so would mean to actually calculate pi(x) for x about 10^316. The best current method has a time complexity of O(x/(ln x)^3) and a storage complexity of O(x^(1/2)/(ln x)). -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Han de Bruijn on 31 Oct 2006 10:41 stephen(a)nomail.com wrote: > Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > >>stephen(a)nomail.com wrote: > >>>Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >>> >>>>stephen(a)nomail.com wrote: >>> >>>>>Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >>>>> >>>>>>I'm DOING mathematics. Mathematics is NOT independent of Physics. >>>>> >>>>>5*10^8 m/s + 5*10^8 m/s = 10*10^8 m/s >>> >>>>There are 10 men in a room. Each has a body temperature of 37 Celcius. >>>>This means that the temperature in the room is: 10 x 37 = 370 Celcius. >>>>Satisfied? Or do you rather prefer it in Kelvin? >>> >>>Satisfied? I have no idea what you mean. Either you are agreeing with >>>me or you totally missed my point. [ ... snip ... ] > >>Who is missing who's point? > > As I said, I have no idea what your point was supposed to be. I anwered your nonsense with some nonsense of my own. That's all. > Your example seemed to support my claim that mathematics is > independent of physics. Of course not. If you have three apples and add two other apples to them then you have five apples. The "five" is obtained by addition and not by multiplication. It's easy to come up with a correct physical problem and solve it with the wrong mathematics. As you did. Han de Bruijn
From: stephen on 31 Oct 2006 11:55 Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > stephen(a)nomail.com wrote: >> Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >> >>>stephen(a)nomail.com wrote: >> >>>>Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >>>> >>>>>stephen(a)nomail.com wrote: >>>> >>>>>>Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >>>>>> >>>>>>>I'm DOING mathematics. Mathematics is NOT independent of Physics. >>>>>> >>>>>>5*10^8 m/s + 5*10^8 m/s = 10*10^8 m/s >>>> >>>>>There are 10 men in a room. Each has a body temperature of 37 Celcius. >>>>>This means that the temperature in the room is: 10 x 37 = 370 Celcius. >>>>>Satisfied? Or do you rather prefer it in Kelvin? >>>> >>>>Satisfied? I have no idea what you mean. Either you are agreeing with >>>>me or you totally missed my point. [ ... snip ... ] >> >>>Who is missing who's point? >> >> As I said, I have no idea what your point was supposed to be. > I anwered your nonsense with some nonsense of my own. That's all. Are you saying 5*10^8 m/s + 5*10^8 m/s = 10*10^8 m/s is incorrect? What is wrong with it? >> Your example seemed to support my claim that mathematics is >> independent of physics. > Of course not. If you have three apples and add two other apples to them > then you have five apples. The "five" is obtained by addition and not by > multiplication. It's easy to come up with a correct physical problem and > solve it with the wrong mathematics. As you did. > Han de Bruijn Really? What physical problem did I solve? And why are you talking about physical problems anyway? The balls and vase problem is not a physical problem. Mathematics is perfectly capable of handling non physical problems, despite your cryptic insistence that "mathematics is not independent of physics". Stephen
From: MoeBlee on 31 Oct 2006 13:04
mueckenh(a)rz.fh-augsburg.de wrote: > David Marcus schrieb: > > What do you mean an axiom is "false"? > > An axiom leading to a contradiction when added to a set of axiom which > do not so, is false. Under that definition of 'false', EVERY non-logical sentence is false. That is, under your definition, EVERY sentence that is not a theorem of the predicate calculus alone is false. MoeBlee |