A BLATENT FLAW in Cantor's diag proof
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From: Aatu Koskensilta on 8 Jun 2010 23:50 stevendaryl3016(a)yahoo.com (Daryl McCullough) writes: > I don't think that's correct. There is no teacher that is > capable of explaining anything to Herc. Yet there is no shortage of people strangely willing to give it a try. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Sylvia Else on 9 Jun 2010 00:03 On 9/06/2010 1:50 PM, Aatu Koskensilta wrote: > stevendaryl3016(a)yahoo.com (Daryl McCullough) writes: > >> I don't think that's correct. There is no teacher that is >> capable of explaining anything to Herc. > > Yet there is no shortage of people strangely willing to give it a try. > Er, that's an assumption. People who appear to be attempting to explain something to Herc may in fact be doing something else entirely, such as trying to understand how Herc's mind works. Herc appears to have a diverse set of false beliefs that he expresses on Usenet. What I've been hoping to get is a handle on is whether all of these false beliefs are delusions arising from his mental illness, or whether some of them are just conventional beliefs of falsehoods, of the kind found often enough even in people considered sane. Of course, there may not be a clear line dividing categories of false beliefs. What's disconcerting is how fragile is the brain's grip on reality, such that some obscure chemical imbalance can destroy it. Sylvia.
From: |-|ercules on 9 Jun 2010 00:18 "George Greene" <greeneg(a)email.unc.edu> wrote >> "William Hughes" <wpihug...(a)hotmail.com> wrote >> > Is this digit sequence (which does not have a last 3) >> >> > 33333... >> >> > in this list >> >> > 1 3 >> > 2 33 >> > 3 333 >> > ... >> >> > of sequences (all of which have a last 3). >> >> > Yes or No. > > I said it first. > > > Herc replied (astoundingly) > >> No. > > If you actually believe this, then why do you keep talking about how > having "every digit sequence" MATTERS? THIS LIST HAS EVERY > digit sequence, up to EVERY finite length, MATCHING .33333.... ! > NAME ME ONE POSITION where this list of FINITE strings DOESN'T MATCH > .3333.....! YOU CAN'T!! Yet DESPITE this, .3333.... IS NOT ON THIS > LIST! > YOU YOURSELF JUST SAID SO! > > So why are you having so much trouble noticing that EVEN if you have > EVERY possible FINITE initial sequence somewhere on your list of > computable reals, you still DON'T have mainfinite ones (and you > provably do NOT > have the infinite anti-diagonal, since that PROVABLY DIFFERS from > EVERYthing you DO have > on the list!)? I already explained. This is a CONVERGENT example which easily demonstrates a *new number*. Somehow you disputed that before. The computable sequences DON'T MISS A SEQUENCE. They cover every possible digit sequence combination VERTICALLY 100% and every possible length of every sequence HORIZONTALLY 100% Now go back to your dismal "BUT COMPUTERS ARE FINITE" argument, it's really aptly stupid even for you. GEORGE LISTEN UP. Superinfinity is not proved by fundamental axioms. There are 3 (NOW 4) reasons that SUPPORT such a ridiculous XEN theory. 1. the antidiagonal makes a new sequence on finite lists. 2. 0.3, 0.33, 0.333 doesn't mean 0.3.. is on the list, so who cares about finite subsequences? 3. halt-omega isn't computable 4. a computer can't calculate infinite digits anyway You can go from one to the other, you can quote "the antidiagonal is a new number" as a reason to justify why "the antidiagonal is a new number", you can dispute a list of every (FINITE) digit sequence exists, you can back up Hughes argument where he agreed with the proposition you deny, you can say "WE PROVED IT" until the cows come home, but you CAN'T find a new sequence of digits when they're all computable to the infinite amount of finite lengths. Herc
From: |-|ercules on 9 Jun 2010 00:31 "Tim Little" <tim(a)little-possums.net> wrote > On 2010-06-09, |-|ercules <radgray123(a)yahoo.com> wrote: >> You seem to be backpedaling like the others now, that a computable >> list is impossible anyway so I can't use it in my argument. > > There is such a concept as a computable list. Unfortunately for your > pronouncements, no computable list can contain all of the computable > reals. Just as certainly, no computable list can contain all the > reals. > > > - Tim putting the word certainly in there makes it seem so manly Here's my computable reals list. The pos digit of the index real is UTM(index, pos) mod 10 It contains every computable real number, and THAT'S for CERTAIN! Herc
From: |-|ercules on 9 Jun 2010 00:44
"Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote > |-|ercules says... >> >>"Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote ... >>> Here's what's funny about USENET. In a regular classroom, >>> you have one teacher and many students. In a typical USENET >>> discussion, there are many teachers and just one student. >>> You'd think that such a low student/teacher ratio would make >>> for quick progress, but that doesn't turn out to be the case. >>> Herc's ignorance can defeat any number of teachers, no matter >>> how knowledgeable and patient. > >>If one of the 'teachers' would just answer my questions instead >>of putting their fingers in their ears and reading maths scripture >>then maybe we could work together on a what Cantor's proofs entail. > > Some questions indicate that the student lacks certain pre-requisites. > In particular, some questions are incoherent. The highest priority in > that case is not to answer the question (an incoherent question cannot > have any coherent answer) but to get the student to ask a *better* > question, one that *can* be given a coherent answer. > >>TRUE or FALSE >> >>1/ no box of the box numbers not in their own boxes proves higher >>infinities > > The reason that's an incoherent question is because facts don't prove > things. A proof is a *demonstration* that a claim is true. > > Your thought experiment with boxes is an incoherent mess, but it > can be fixed with a little work. Let's try to fix it. > > You want to say that > > 1. There is a collection of boxes. > 2. Each box contains zero, one or more naturals. > 3. Each box is labeled with a natural number. > > Okay, let's define a box to be "self-contained" if > b contains its own label. Let C' be the set of all > boxes that are *not* self-contained. Finally, let > D be the set of all labels for boxes in C'. > > Then it immediately follows that D is not the contents > of any single box. > > From this, it follows that there exists a set of naturals > that is not equal to the contents of any box. So there are > "more" sets of naturals than there are boxes. This is true > *regardless* of how many boxes there are, or what naturals > are contained by which boxes, as long as each box has a > label. > > So we conclude: there are more sets of naturals than there > are naturals. > >>2/ all possible digit sequences are computable to all, as in an infinite amount >>of, finite lengths > > Once again, a completely incoherent mess. What is true, as I > have already said, is this: > > For all reals r, for all natural number n, there exists a computable > real r' such that r and r' agree on the first n digits. > > But the following, similar statement is false: > > For all reals r, there exists a computable real r' such that > for all natural numbers n, r and r' agree on the first n digits. > >>ANY form of EVASION and not ANSWERING the questions will be discarded. > > You are a very poor student. You ask incoherent questions, and then > expect to get coherent answers. Sometimes the correct is: Your questions > are incoherent. It is your aversion to express your fundamentally flawed mathematical assertions into ENGLISH that causes you to MISS blatant errors in those assertions. There is NOTHING wrong with this statement. You don't accept it because it clearly shows Cantor's proof is nonsense, as do the MANY CORRECT formulations of Cantor's proof in a single sentence about boxes. >>2/ all possible digit sequences are computable to all, as in an infinite amount >>of, finite lengths How can it possibly be a "completely incoherent mess" when you are able to formalize it, and several sci.math posters stated it was TRUE? Are you an idiot or just a blatant LIAR Daryl? Herc |