A BLATENT FLAW in Cantor's diag proof
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From: Virgil on 12 Jun 2010 02:25 In article <e0b9ecf0-1b9f-462b-8bf5-888bf21d85e8(a)g1g2000pro.googlegroups.com>, Pol Lux <luxpol5(a)gmail.com> wrote: > Hey guys, you are not taking me seriously, are you? You are scaring > me! I was just being ironic, you know... Your irony is much too rusty.
From: Daryl McCullough on 12 Jun 2010 09:43 |-|ercules says... >I understand fully every point made against me. I also happen to see >the error in your posts. If that were true, then you could easily show it. Give the standard proof of the uncountability of the reals, in a form that a mathematician would agree: yes, that's a correct proof. It should take the form of a sequence of statements such that each statement is either a definition, an accepted mathematical fact, or follows from previous statements by accepted rules of inference. Then, what you need to do is to point out which step is incorrect. If you really gave a proof, that means that either you find an axiom (an accepted fact of mathematics) that you disagree with, or you find an accepted rule of inference that you disagree with. Then, you need to explain *why* you disagree with that axiom or rule of inference. The most convincing explanation would be a proof (in the sense that mathematicians would consider it a proof) that the questionable axioms and/or rules of inference lead to a contradiction. Short of that, you can show that they lead to a conclusion that is contrary to other statements you feel ought to be true (even if they are not provable). You have not done either of these. You haven't shown that standard mathematical axioms and rules of inference lead to a contradiction. You have not proposed alternative axioms that standard mathematics conflicts with. The fact that you've done neither of these, and still claim to have discovered a "blatant flaw" in Cantor's proof, shows that you are mistaken. You don't understand Cantor's proof. -- Daryl McCullough Ithaca, NY
From: |-|ercules on 12 Jun 2010 11:07 "Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote > |-|ercules says... > >>I understand fully every point made against me. I also happen to see >>the error in your posts. > > If that were true, then you could easily show it. Give the standard > proof of the uncountability of the reals, in a form that a mathematician > would agree: yes, that's a correct proof. It should take the form of > a sequence of statements such that each statement is either a definition, > an accepted mathematical fact, or follows from previous statements by > accepted rules of inference. > > Then, what you need to do is to point out which step is incorrect. > If you really gave a proof, that means that either you find an axiom > (an accepted fact of mathematics) that you disagree with, or you find > an accepted rule of inference that you disagree with. > > Then, you need to explain *why* you disagree with that axiom or rule > of inference. The most convincing explanation would be a proof (in > the sense that mathematicians would consider it a proof) that the > questionable axioms and/or rules of inference lead to a contradiction. > > Short of that, you can show that they lead to a conclusion that is > contrary to other statements you feel ought to be true (even if they > are not provable). > > You have not done either of these. You haven't shown that > standard mathematical axioms and rules of inference lead > to a contradiction. You have not proposed alternative axioms > that standard mathematics conflicts with. > > The fact that you've done neither of these, and still claim to > have discovered a "blatant flaw" in Cantor's proof, shows that > you are mistaken. You don't understand Cantor's proof. > > -- > Daryl McCullough > Ithaca, NY > I accept your challenge! Cantor's diag proof - by Herc! Take any list of real expansions 123 456 789 Diag = 159 Anti-Diag = 260 VOILA - SUPERINFINITY! Herc
From: Pol Lux on 12 Jun 2010 11:10 On Jun 12, 8:07 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "Daryl McCullough" <stevendaryl3...(a)yahoo.com> wrote > > > > > > > |-|ercules says... > > >>I understand fully every point made against me. I also happen to see > >>the error in your posts. > > > If that were true, then you could easily show it. Give the standard > > proof of the uncountability of the reals, in a form that a mathematician > > would agree: yes, that's a correct proof. It should take the form of > > a sequence of statements such that each statement is either a definition, > > an accepted mathematical fact, or follows from previous statements by > > accepted rules of inference. > > > Then, what you need to do is to point out which step is incorrect. > > If you really gave a proof, that means that either you find an axiom > > (an accepted fact of mathematics) that you disagree with, or you find > > an accepted rule of inference that you disagree with. > > > Then, you need to explain *why* you disagree with that axiom or rule > > of inference. The most convincing explanation would be a proof (in > > the sense that mathematicians would consider it a proof) that the > > questionable axioms and/or rules of inference lead to a contradiction. > > > Short of that, you can show that they lead to a conclusion that is > > contrary to other statements you feel ought to be true (even if they > > are not provable). > > > You have not done either of these. You haven't shown that > > standard mathematical axioms and rules of inference lead > > to a contradiction. You have not proposed alternative axioms > > that standard mathematics conflicts with. > > > The fact that you've done neither of these, and still claim to > > have discovered a "blatant flaw" in Cantor's proof, shows that > > you are mistaken. You don't understand Cantor's proof. > > > -- > > Daryl McCullough > > Ithaca, NY > > I accept your challenge! > > Cantor's diag proof - by Herc! > > Take any list of real expansions > > 123 > 456 > 789 > > Diag = 159 > Anti-Diag = 260 > > VOILA - SUPERINFINITY! > > Herc It's wonderful to be able to see infinity so clearly in those 3 lines of 3 numbers. Remarkable.
From: Aatu Koskensilta on 12 Jun 2010 11:10
George Greene <greeneg(a)email.unc.edu> writes: > You may do as you like, but anything you do in public has the > property that you must surely have thought it might have some > effect on the outside world, an effect somehow causally connected > to your enjoyment of having done it. Well, I was just hoping to prod you into thinking about these matters more carefully, trusting that you would sort out your confusion on your own. It was, in a word, just a gentle hint. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |