Cantor Confusion
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From: Han.deBruijn on 15 Oct 2006 13:03 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. Han de Bruijn
From: Han.deBruijn on 15 Oct 2006 13:10 Tony Orlow schreef: > 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. > > 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? :) Hey, Tony, sometimes I cannot improve on you! Han de Bruijn
From: Han.deBruijn on 15 Oct 2006 13:23 Dik T. Winter schreef: > 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. But, ah, Dik and others, you should _know_ that by now! After having endured my sci.math postings since 1989. I've posted essentially the same message over and over again for more than 15 years! Han de Bruijn
From: Han.deBruijn on 15 Oct 2006 13:27 Dik T. Winter schreef: > In article <1160856895.115824.134080(a)b28g2000cwb.googlegroups.com> > Han.deBruijn(a)DTO.TUDelft.NL writes: > > stephen(a)nomail.com schreef: > > > Dik T. Winter <Dik.Winter(a)cwi.nl> wrote: > ... > > > > Pray warn me when 2 has changed sufficiently to be the square of a > > > > rational. > > > > I would not like to miss that moment. > > > > > > The day the circle is squared cannot be to far behind. > > > > 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? Han de Bruijn
From: Han.deBruijn on 15 Oct 2006 13:33
Dik T. Winter schreef: > In article <1160856043.795135.198610(a)h48g2000cwc.googlegroups.com> > Han.deBruijn(a)DTO.TUDelft.NL writes: > > > (BTW, I find > > Banach Spaces not very useful either) > > They are (as far as I know) used in the design of methods to solve partial > differential equations. Right. They are supposed to be basic for the Finite Element Method, to be precise. But I have done quite some Finite Elements myself, and my judgement is that they are not very basic. Here you can read what stuff IMO is basic: http://hdebruijn.soo.dto.tudelft.nl/jaar2004/purified.pdf http://www.xs4all.nl/~westy31/Electric.html#Irregular http://hdebruijn.soo.dto.tudelft.nl/hdb_spul/belgisch.pdf Han de Bruijn |