Obections to Cantor's Theory (Wikipedia article)
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From: Robert Kolker on 28 Jul 2005 06:40 Virgil wrote: > > TO has yet to produce any axiom system of his own, and, judging by the > quality of his arguments, is extremely unlikely ever to be able produce > one of any value. Orlow is a mathematical incompetent. In addition to this, his arrogant ignorance of mathematics has indicated stupidity. Not knowing something is no shame, as we are all born ignorant. Refusal to learn is the mark of the Truly Stupid. Bob Kolker
From: Robert Kolker on 28 Jul 2005 06:45 Han de Bruijn wrote: > > Since sets aren't physical, since straight lines aren't physical, since > numbers aren't physical. Of course they _are_ physical. Or better: they > _were_ physical. Though some have been more physical than others. Those > which have been more physical are the better ones, i.e. straight lines. What is a straight line? Are there any straightlines on the surface of an n-sphere for n > 2? When are you going to learn mathematics? It lacks grace to criticize that of which you are totally ignorant. You not only are ignorant, your are as dumb as a bag of rocks. Search the physical world over and you will not find a line, a curve or the number two. > Heh, heh. That's precisely the first thing I want: throw _doubt_ upon > everything that everybody finds so certain. And I thought that I have > indicated that well enough, all over the place, ever since 1989. You are throwing spew, not doubt. You want to discredit a mathematical theory? Show that it is internally inconsistent. This you have not done. > > As a consequence, mathematics can no longer be founded on set theory. > That's precisely what I want: set theory as a relatively _unimportant_ > branch of mathematics. Most of mathematics is grounded on set theory. Without set theory there would be no topology, no theory of real or complex numbers and no theory of manifolds. Once again, you show your ignorance borders on stupidity. Bob Kolker
From: Han de Bruijn on 28 Jul 2005 07:35 Robert Kolker wrote: > Most of mathematics is grounded on set theory. Without set theory > there would be no topology, no theory of real or complex numbers > and no theory of manifolds. Simply not true. Real and complex numbers existed well before the advent of set theory. Have some doubts with the rest. But, anyway, I _didn't_ say that set theory should be abandoned altogether. > Once again, you show your ignorance borders on stupidity. Look what your "arguments" look like. (And you're not the only one.) If this kind of "logic" is representative for mainstream mathematics, how do you ever expect that we would want to participate? Han de Bruijn
From: Martin Shobe on 28 Jul 2005 07:37 On Thu, 28 Jul 2005 10:47:43 +0200, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >> But that doesn't mean that the sets are real, or that the >> chords are really sets. All it means is that you have >> created an abstraction of chords in terms of sets. >Now tell this to a man in the street and ask him if he understands you. Does that really matter? If I were to explain what I do when tracking down bugs to the man in the street, I would get a glazed look in response. >Whatever. It means that you can go back to earth. Because, in the end, >you can _hear_ the music. But you cannot go back to earth with _all_ of >the set theory in mathematics. And _that_ is the gist of my argument. And the gist of our argument is that not being able to "go back to earth" is not a problem. Mathematics is not restricted to those things that can "go back to earth". Martin
From: Dik T. Winter on 28 Jul 2005 07:39
In article <MPG.1d51bac9dec3f89b989fcc(a)newsstand.cit.cornell.edu> Tony Orlow (aeo6) <aeo6(a)cornell.edu> writes: > Dik T. Winter said: .... > > Well, bijections provide an excellent way to compare sets, because it is > > an equivalence relation, and so they define equivalence classes. > > The denote equivalence for finite sets, and some kind of relation for > infinite sets, but not necessarily equivalence. Eh? Bijections are reflexive, transitive and symmetric, so they are an equivalence relation by the definition of the term equivalence relation. > > Pray explain your mapping, it is not clear. > > Define each subset as an infinite binary string, where the first bit denotes > membership of the first natural, the second bit denotes membership of the > second natural, etc. Each subset int he pwoer set of the naturals is thus > represented by a unique infinite binary string. Each finite binary string is > accepted as corresponding to a finite natural, but the infinite strings, with > infinite values, are rejected on the basis that natural numbers cannot have > infinite values. Indeed. > If they were allowed to have infinite values, the the set > of all infinite binary strings which represents the power set of the > naturals could be put in bijection with the set of natural numbers, and you > would have a bijection between the naturals and their power set. Only those binary strings that correspond to the finite naturals. How about the binary strings that correspond to the infinite naturals? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ |