Obections to Cantor's Theory (Wikipedia article)
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From: Alec McKenzie on 19 Jul 2005 17:29 Chan-Ho Suh <suh(a)math.ucdavis.nospam.edu> wrote: > In article <mckenzie-E70336.17334819072005(a)news.aaisp.net.uk>, Alec > McKenzie <mckenzie(a)despammed.com> wrote: > > > David Kastrup <dak(a)gnu.org> wrote: > > > > > Alec McKenzie <mckenzie(a)despammed.com> writes: > > > > > > > David Kastrup <dak(a)gnu.org> wrote: > > > > > > > >> Alec McKenzie <mckenzie(a)despammed.com> writes: > > > >> > It has been known for a proof to be put forward, and fully accepted > > > >> > by the mathematical community, with a fatal flaw only spotted years > > > >> > later. > > > >> > > > >> In a concise 7 line proof? Bloody likely. > > > > > > > > I doubt it had seven lines, but I really don't know how many. > > > > Probably many more than seven. > > > > > > It was seven lines in my posting. You probably skipped over it. > > > > I see you have misunderstood what I said. You seemed to be > > denying that the accepted proof I mentioned (that turned out to > > have a flaw) was only seven lines, and I was merely saying that > > I didn't know how many lines it had. > > Aha, so you're saying you had a particular proof in mind? Well, let's > hear which one it is. Of course I had a particular proof in mind: In 1879 a proof of the four-colour map theorem was published by Arthur Bray Kemp, a member of the London Mathematical Society. He became a member of the Royal Society in consideration for his achievement. It was not until eleven years later, in 1890, that the fatal flaw in the proof was pointed out by Percy John Heawood in a paper in the Quarterly Journal of Mathematics. -- Alec McKenzie mckenzie(a)despammed.com
From: G. Frege on 19 Jul 2005 17:40 On 19 Jul 2005 14:05:16 -0700, "david petry" <david_lawrence_petry(a)yahoo.com> wrote: > > > > There is no mention of one historical or living figure who is > > anti-Cantorian, what their objections were > > > Hmm, not quite. I did mention Kronecker. Did you miss that? > Then write an article about /Intuitionism/ - or better read one about it. http://en.wikipedia.org/wiki/Intuitionism It's a rather bad idea to tie Kronecker to those ignorant and unscholared crowd of so called "anti-Cantorians" [i.e. mathe- matical cranks] showing up in USENET these days. F.
From: Chan-Ho Suh on 19 Jul 2005 17:43 In article <mckenzie-27AD7F.22290719072005(a)news.aaisp.net.uk>, Alec McKenzie <mckenzie(a)despammed.com> wrote: > Chan-Ho Suh <suh(a)math.ucdavis.nospam.edu> wrote: > > > In article <mckenzie-E70336.17334819072005(a)news.aaisp.net.uk>, Alec > > McKenzie <mckenzie(a)despammed.com> wrote: > > > > > I see you have misunderstood what I said. You seemed to be > > > denying that the accepted proof I mentioned (that turned out to > > > have a flaw) was only seven lines, and I was merely saying that > > > I didn't know how many lines it had. > > > > Aha, so you're saying you had a particular proof in mind? Well, let's > > hear which one it is. > > Of course I had a particular proof in mind: > > In 1879 a proof of the four-colour map theorem was published by > Arthur Bray Kemp, a member of the London Mathematical Society. > He became a member of the Royal Society in consideration for his > achievement. > > It was not until eleven years later, in 1890, that the fatal > flaw in the proof was pointed out by Percy John Heawood in a > paper in the Quarterly Journal of Mathematics. That's a good example. But it's inaccurate to say he became an FRS because of this. The four color theorem was not so distinguished then and had only been formulated a short time before. Rather, his membership rested on his work in physics. It's because of Kempe's failure and other attempts that the four color theorem became more famous. Also, if this is your best example, then it's not very convincing for the points you are trying to make. Kempe's mistake was in trying to extend his five color theorem to four colors; he made a mistake in a complicated enumeration of cases. That happens a lot in situations like that. It's certainly not comparable at all to the case under discussion: Cantor's theorem that a powerset of a set has higher cardinality. And as I alluded to in another post, I seriously doubt Kempe's paper underwent serious scrutiny by many people.
From: Stephen Montgomery-Smith on 19 Jul 2005 17:51 Tony Orlow (aeo6) wrote: > I was asked that before, and never got around to fully analyzing the axioms for > lack of time, but the diagonal proof suffers from the fatal flaw of assuming > that the diaginal traversal actually covers all the numbers in the list. Any > complete list of digital numbers of a given length, even a given infinite > length, is exponentially longer in members than wide in terms of the digits in > each member. Therefore, the diagonal traversal only shows that the anti- > diagonal does not exist in the first aleph_0 terms. Of course, the entire list > is presumed to be aleph_1 long, being a list of the reals, and the antidiagonal > simply exists on the list, below the line of diagonal traversal. Cantorians > seem to think infinity is simply infinity, even during the course of a proof > that that is not the case. I got it!!! The usual proof starts - suppose that there is a complete countable list of real numbers. But your rebuttal is amazing in its simplicity - suppose that there isn't. Have you considered the usual proof that there are infinitely many prime numbers? I think your method might also work to reveal the flaw there as well.
From: Jesse F. Hughes on 19 Jul 2005 17:38
"david petry" <david_lawrence_petry(a)yahoo.com> writes: > Jesse F. Hughes wrote: > >> This isn't about >> "anti-Cantorians", whatever the hell that might mean. This is about >> Petrians, a well-defined group in which there is no dissension at all >> (since there is only one member). > > Uh, not quite. For example, in this discussion, Han deBruijn > seems to understand and agree with almost everything I say. Wow. You must be proud. You still haven't clarified what Cantor's theory is. Since you claim to be a critique of Cantor's theory, perhaps you should tell us what it is. -- Jesse F. Hughes "The three principal virtues of a programmer are Laziness, Impatience, and Hubris."-- Larry Wall in the Perl5 Manpages |