Cantor Confusion
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From: stephen on 14 Oct 2006 21:51 David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > 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? I am guessing that he means that if all of mathematics does not bow to his will, he would prefer mathematics not to exist at all. You are either with Han, or you are against him. His holy jihad can know no compromise. Stephen
From: Tony Orlow on 14 Oct 2006 22:38 stephen(a)nomail.com wrote: > David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >> 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? > > I am guessing that he means that if all of mathematics does > not bow to his will, he would prefer mathematics not to exist > at all. You are either with Han, or you are against him. > His holy jihad can know no compromise. > > Stephen You fellers sure are dense. Han's simply saying that the universe is consistent, or it doesn't exist at all. Clearly, it exists, so obviously it's not self-contradictory. Where there is a conflict between notions, where there is paradox, there is also explanation. One has to choose the most consistent path, while integrating the widest array of ideas possible. Hey, Han, is that about right? :) TOny
From: Tony Orlow on 14 Oct 2006 22:39 Alan Morgan wrote: > In article <1160858900.410979.56520(a)m7g2000cwm.googlegroups.com>, > <mueckenh(a)rz.fh-augsburg.de> wrote: >> Alan Morgan schrieb: >> >>>> But sqrt(-1) does not yield contradictions, as far as I know. >>> It violates the heck out of my intuition. The objections to set >>> theory seem to arise from someone's dislike for the conclusions >>> or an inability to do mathematics correctly. >> Is Weyl this someone? "...classical logic was abstracted from the >> mathematics of finite sets and their subsets...Forgetful of this >> limited origin, one afterwards mistook that logic for something above >> and prior to all mathematics, and finally applied it, without >> justification, to the mathematics of infinite sets. This is the Fall >> and original sin of [Cantor's] set theory ..." > > And David Hilbert said "No one will drive us from the paradise > which Cantor created for us". > > Alan Yes, he said that while cringing in a cave. I think he said it to Plato. :) TOny
From: Dik T. Winter on 14 Oct 2006 22:48 In article <1160835375.441299.190640(a)f16g2000cwb.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: > Dik T. Winter schrieb: .... > > Oh. So you think that Banach spaces are not very useful? You think that > > a book like "The Algebraic Eigenvalue Problem" is not very useful? You > > may note that both are heavily based on set theory. > > Only by accident, mainly because of Bourbaki. In, say, 2020, there will > be Algebra but without any transfinite set theory. In what way does "The Algebraic Eigenvalue Problem" rely on Bourbaki? I think you have no idea what that book is about. Have your read it, ever? Look around in the library of your university for J. H. Wilkinson, "The Algebraic Eigenvalue Problem". And after you have read it, tell me in what way it depends on Bourbaki. You are just spouting nonsense. That book is the starting point for numerical mathematics. -- 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 14 Oct 2006 22:57
In article <1160852959.173914.326370(a)e3g2000cwe.googlegroups.com> Han.deBruijn(a)DTO.TUDelft.NL writes: > Almost. Any function which is defined everywhere at an interval of real > numbers is also continuous at the same interval. Or, with other words: > For real valued functions, being defined is very much the same as being > continuous. This fact is known as Brouwer's Continuity Theorem: > > http://www.andrew.cmu.edu/user/cebrown/notes/vonHeijenoort.html#Brouwer2 > > Brouwer's Continuity Theorem is cosmologically valid. Yes, when you go intuitionistic. With intuitionistic reasoning, I think that the entier function is not a function. Something similar can be done with Anders Kock's methods. But pray state when you are arguing in anything other than standard mathematics. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ |