A BLATENT FLAW in Cantor's diag proof
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From: Aatu Koskensilta on 12 Jun 2010 11:12 George Greene <greeneg(a)email.unc.edu> writes: > Herc, unfortunately, though, is not serious about understanding > anything. Why then bother explaining anything to him? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: |-|ercules on 12 Jun 2010 12:05 "Pol Lux" <luxpol5(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
From: Jesse F. Hughes on 12 Jun 2010 12:36 "|-|ercules" <radgray123(a)yahoo.com> writes: > 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! I must say that this proof *does* seem fishy. -- Jesse F. Hughes "Love songs suck and losing you ain't worth a damn." -- The poetry of Bad Livers
From: |-|ercules on 12 Jun 2010 12:54 "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote > "|-|ercules" <radgray123(a)yahoo.com> writes: > >> 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! > > I must say that this proof *does* seem fishy. > We can reproof it! Better than it was before... The anti-diagonal function is a two-place function f(L,n) which returns a digit for each list L and for each natural number n. It's a simple function: First define a transformation on digits c(d) as follows: c(5) = 4. If d is not equal to 5, then c(d) = 5. Now, we define f(L,n) as follows: f(L,n) = c(L(n,n)) where L(n,n) = the nth digit of the nth real in the list L. Now, the antidiagonal real is defined by: antiDiag(L) = that real r such that the integer part of r is 0, and forall n, the nth digit of r is equal to f(L,n). This is a function that given any list of reals L, returns another real, antiDiag(L), which is guaranteed to not be on the list L. There is nothing self-referential about this definition. Let's let L be the list containing the falling reals: L_0 = 0.000... L_1 = 0.300... L_2 = 0.3300... L_3 = 0.3330... etc. Then the antidiagonal will be 0.555... This is clearly not on list L. Therefore SUPERINFINITY Herc
From: Pol Lux on 12 Jun 2010 14:37
On Jun 11, 11:25 pm, Virgil <Vir...(a)home.esc> wrote: > In article > <e0b9ecf0-1b9f-462b-8bf5-888bf21d8...(a)g1g2000pro.googlegroups.com>, > Pol Lux <luxp...(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. I'll let you all have fun debating endlessly how Cantor was wrong. Don't forget also that Einstein was stupid, and that all mathematicians are wrong, except JSH, who is actually God, and what else? That integer numbers don't exist, nor do negative numbers, and infinity is wrong in the foundations, but j-jercules will save from that, and... whatever. Just boring and meaningless. Please all take your medication. Thank you. |