A BLATENT FLAW in Cantor's diag proof
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From: Daryl McCullough on 12 Jun 2010 18:45 |-|ercules says... >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! Okay, so the first part of the challenge was to see if you could give the standard proof of the uncountability of the reals. You failed that part. The second part is to demonstrate what was wrong with the proof in the first part. But you don't actually know how to do the first part. So you were not telling the truth when you said that you understood the standard proof. -- Daryl McCullough Ithaca, NY
From: |-|ercules on 12 Jun 2010 18:54 "Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote ... > |-|ercules says... > >>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! > > Okay, so the first part of the challenge was to see > if you could give the standard proof of the uncountability > of the reals. You failed that part. > > The second part is to demonstrate what was wrong with > the proof in the first part. > > But you don't actually know how to do the first part. > So you were not telling the truth when you said that > you understood the standard proof. > Didn't you see my reproof, better than that one? Herc
From: Pol Lux on 12 Jun 2010 19:31 On Jun 12, 9:05 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "Pol Lux" <luxp...(a)gmail.com> wrote ... > > > > > > > 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. > > Listen buddy, does 260 equal the first real? > Does 260 equal the second real? > Does 260 equal the third real? > > There, that proves it! Wait there's more, the consistency of mum's pudding > proves the nonconsistency of FireFox and the consistent consistency proofs > prove that consistency proofs prove consistency consistently. > > Herc Hey Herc, you are a piece of work. As a standup comedian, you might have a chance, maybe. I just hope you are aware of what you are saying. If not, it's really tragic.
From: |-|ercules on 12 Jun 2010 19:43 "Pol Lux" <luxpol5(a)gmail.com> wrote ... > On Jun 12, 9:05 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> "Pol Lux" <luxp...(a)gmail.com> wrote ... >> >> >> >> >> >> > 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. >> >> Listen buddy, does 260 equal the first real? >> Does 260 equal the second real? >> Does 260 equal the third real? >> >> There, that proves it! Wait there's more, the consistency of mum's pudding >> proves the nonconsistency of FireFox and the consistent consistency proofs >> prove that consistency proofs prove consistency consistently. >> >> Herc > > Hey Herc, you are a piece of work. As a standup comedian, you might > have a chance, maybe. I just hope you are aware of what you are > saying. If not, it's really tragic. Not as tragic as the mass hallucination of superinfinity, based on the *new* 260 above and no box containing the box numbers of boxes not contained in their own box. Herc
From: Daryl McCullough on 12 Jun 2010 19:54
|-|ercules says... > >"Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote ... >> |-|ercules says... >> >>>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! >> >> Okay, so the first part of the challenge was to see >> if you could give the standard proof of the uncountability >> of the reals. You failed that part. >> >> The second part is to demonstrate what was wrong with >> the proof in the first part. >> >> But you don't actually know how to do the first part. >> So you were not telling the truth when you said that >> you understood the standard proof. >> > >Didn't you see my reproof, better than that one? You claimed to accept my challenge, and you failed. That shows that you don't understand the subject. -- Daryl McCullough Ithaca, NY |