Obections to Cantor's Theory (Wikipedia article)
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From: Chan-Ho Suh on 19 Jul 2005 18:18 In article <mckenzie-5A92EB.23042519072005(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-27AD7F.22290719072005(a)news.aaisp.net.uk>, Alec > > McKenzie <mckenzie(a)despammed.com> wrote: > > > > > 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. > > I did not say he became an FRS because of this. I would be very > surprised if he ever did become an FRS at all. > Sorry, my mistake. You are right that you did not say that. But you did say he became a member because of the four color theorem. I believe this is misleading because his MacTutor bio states it was his work in kinematics that was considered. He did become a Fellow soon after though. He was a pretty distinguished guy...eventually became President of the London Mathematical Society. I'm surprised you hold him in so little esteem.
From: Chan-Ho Suh on 19 Jul 2005 18:18 In article <mckenzie-5A92EB.23042519072005(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-27AD7F.22290719072005(a)news.aaisp.net.uk>, Alec > > McKenzie <mckenzie(a)despammed.com> wrote: > > > > > 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. > > I did not say he became an FRS because of this. I would be very > surprised if he ever did become an FRS at all. > Sorry, my mistake. You are right that you did not say that. But you did say he became a member because of the four color theorem. I believe this is misleading because his MacTutor bio states it was his work in kinematics that was considered. He did become a Fellow soon after though. He was a pretty distinguished guy...eventually became President of the London Mathematical Society. I'm surprised you hold him in so little esteem.
From: Barb Knox on 19 Jul 2005 18:26 In article <MPG.1d4726e11766660c989f2f(a)newsstand.cit.cornell.edu>, Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: [snip] >Infinite whole numbers are required for an infinite set of whole numbers. Good grief -- shake the anti-Cantorian tree a little and out drops a Phillite. Here's a clue: ALL whole numbers are finite. Here's a (2nd-order) proof outline, using mathematical induction (which I assume/hope you accept): 0 is finite. If k is finite then k+1 is finite. Therefore all natural numbers are finite. -- --------------------------- | BBB b \ Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum viditur. | BBB aa a r bbb | -----------------------------
From: stephen on 19 Jul 2005 19:58 In sci.math Barb Knox <see(a)sig.below> wrote: > In article <MPG.1d4726e11766660c989f2f(a)newsstand.cit.cornell.edu>, > Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > [snip] >>Infinite whole numbers are required for an infinite set of whole numbers. > Good grief -- shake the anti-Cantorian tree a little and out drops a > Phillite. Here's a clue: ALL whole numbers are finite. Here's a > (2nd-order) proof outline, using mathematical induction (which I > assume/hope you accept): > 0 is finite. > If k is finite then k+1 is finite. > Therefore all natural numbers are finite. Talking to Tony is a waste of time. He does not understand induction and is a firm believer in "after infinity". He is a fine example of the non-mathematical sort who complains about Cantor. Stephen
From: stephen on 19 Jul 2005 20:02
In sci.math Stephen Montgomery-Smith <stephen(a)math.missouri.edu> wrote: > 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. Don't waste your breath. You are talking to someone who thinks there are only a finite number of finite prime numbers. Stephen |