CANTOR DISPROOF <<<<<<<<<<<<<<<<
in [Logic]
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From: Nam Nguyen on 22 Jun 2010 01:15 Transfer Principle wrote: > If one feels that uncountability is a useful concept, then > one is free to use a theory such as ZFC in which the > existence of uncountable sets is provable. Sure. > That same freedom > should be granted to those like Herc who believe that > uncountability is a useless concept. Sure. He's free not to use ZFC for anything. > He should be allowed to > oppose Cantor's Theorem without five-letter insults. Five-letter insult or not, he's not just opposing Cantor's Theorem and he's not just opposing the whole FOL proof machinery: he's inconsistent in reasoning! He either should accept FOL proof machinery or disregard it entirely, but once he accepts it he has to accept the proof of Cantor's theorem and that has nothing to do with his seeing the theorem as useful or useless. We should NOT support any kind of inconsistency in reasoning.
From: Graham Cooper on 22 Jun 2010 02:49 On Jun 22, 3:15 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Transfer Principle wrote: > > If one feels that uncountability is a useful concept, then > > one is free to use a theory such as ZFC in which the > > existence of uncountable sets is provable. > > Sure. > > > That same freedom > > should be granted to those like Herc who believe that > > uncountability is a useless concept. > > Sure. He's free not to use ZFC for anything. > > > He should be allowed to > > oppose Cantor's Theorem without five-letter insults. > > Five-letter insult or not, he's not just opposing Cantor's > Theorem and he's not just opposing the whole FOL proof machinery: > he's inconsistent in reasoning! He either should accept FOL > proof machinery or disregard it entirely, but once he accepts > it he has to accept the proof of Cantor's theorem and that > has nothing to do with his seeing the theorem as useful or useless. > > We should NOT support any kind of inconsistency in reasoning. What BS. I have made 3 main valid complaints on transfiniteness 1 the powerset proof is essentially no box contains the box numbers (of boxes) that don't contain their own box number. You honestly think this is a great breakthrough? 2 the diag proof is essentially in general form An AD(n) =/= L(n,n) -> An AD(n) =/= L(n,n) it does NOT necessarily generate any new digit sequence IN FACT 3 It takes 10^x reals to list every permutation of digits x digits wide So with infinite reals you can list Every permutation of digits infinite digits wide. This is a concrete contradiction to the claims of Cantor's proof. It is not me getting it wrong. You won't even acknowledge these facts in blind faith of ZFC.
From: Graham Cooper on 22 Jun 2010 02:52 On Jun 22, 11:56 am, Sylvia Else <syl...(a)not.here.invalid> wrote: > On 22/06/2010 11:41 AM, herbzet wrote: > > > > > > > > > Sylvia Else wrote: > >> herbzet wrote: > > >>> Herc is a troll who is HAVING A BALL jerking all the "smart guys" around. > > >> Or not. Herc is a paranoid schizophrenic, and subject to a variety of > >> delusions. > > > None of which implies that he is not also a troll. > > >> What isn't clear is whether this Cantor stuff is a > >> conventional misunderstanding, or yet another delusion. > > > It's the same old tired Cantor troll b.s. > > I didn't realise before how long this has been going on for. > > But I don't think he's a troll - he appears to have a genuine belief > that the world's mathematicians have got this wrong. If it's a > conventional misunderstanding, he might yet be persuaded that he is > mistaken. But if, as I increasingly suspect, it's a delusion, then it > will be immune to any kind of disproof. His behaviour here is consistent > with his behaviour when discussing his other delusions - the closer you > get to attacking his core belief, the more abusive he becomes. > > I've never heard of anyone having a delusion about mathematics before. > > Sylvia. Your idea of knocking my core belief is calling me deluded Herc
From: Mike Terry on 22 Jun 2010 13:42 "Sylvia Else" <sylvia(a)not.here.invalid> wrote in message news:88ajhvF3kjU1(a)mid.individual.net... > On 22/06/2010 11:41 AM, herbzet wrote: > > > > > > Sylvia Else wrote: > >> herbzet wrote: > >> > >>> Herc is a troll who is HAVING A BALL jerking all the "smart guys" around. > >> > >> Or not. Herc is a paranoid schizophrenic, and subject to a variety of > >> delusions. > > > > None of which implies that he is not also a troll. > > > >> What isn't clear is whether this Cantor stuff is a > >> conventional misunderstanding, or yet another delusion. > > > > It's the same old tired Cantor troll b.s. > > I didn't realise before how long this has been going on for. > > But I don't think he's a troll - he appears to have a genuine belief > that the world's mathematicians have got this wrong. If it's a > conventional misunderstanding, he might yet be persuaded that he is > mistaken. Personally I can't see this ever happening. When I started off with Herc (years ago), it seemed like he was just making a simple mistake, and so it should be easy enough to show where this mistake was. (And indeed it is easy in a mathematical sense...) As I went further, I realised Herc knows nothing of normal mathematical definitions (like um.. like the ones used in Cantor's proofs which he is discussing), and nothing of mathematical reasoning (proofs starting from definitions etc.). Also he has his own unclear (contradictory maybe?) definitions for words he uses. So obviously a bit more work than I first thought! :) Still, I thought if I break everything down into smaller and smaller steps, explain exactly all the definitions involved, get Herc to clarify his own definitions to make them precise etc., then I could still get him to realise he's mistaken. But there is a much more basic problem - Herc actually refuses to engage in "normal mathematical dialog". What I mean is that if you and I discussed something, and I didn't understand a step in your proof, I'd point out what I didn't understand, and you'd go away and expand the proof until I was happy. Similarly, if I used a vague term, you could ask me to clarify it, and I would break it down into well understood basic notions, quantifiers, etc., and we'd move on... Neither of us would be offended by the process or think we were being insulted, it's just business as usual for communicating mathematics. Actually, I've never really thought of this as a "mathematical" skill, as I've always thought of mathematics as being the interesting stuff we do on top of all that. It's a basic skill which I'm sure I had around the age of 10 (once I'd read simple proofs like the infinitude of the primes etc.), although clearly at that age I didn't understand many definitions. Anyway, it's to be expected that posters won't all have the same level of knowledge of working definitions, which is why we have "normal mathematical dialog" to get along! I believe it's impossible to "talk maths" with someone who simply refuses to engage in this behaviour. This includes Herc - I don't believe he will ever respond to a request to clarify something into simpler terms. (Maybe some people's brains just don't work in that analytic way?, and so they don't understand the need for it?) And if you suggest a precise definition for something vague Herc is saying, he will neither confirm nor deny that that is what he meant. (He may even scold you for introducing irrelevent factors into the argument, and suggest you should just ask him to explain, but if you do that of course you won't get much of a clarification!) So what will Herc actually do if you follow my earlier idea of explaining in greater and greater detail, asking for clarifications, refusing to go along with vague confusing terminology until it is clarified and so on? [I thought that surely if I did this thoroughly enough, Herc would have NO CHOICE but to agree where he was wrong, or at least he would have to reply in such a way that it was obvious to himself and others that he was not able to answer the questions and support his claims.] The answer is that Herc will just ignore all your efforts and respond with something vague, unrelated to the detail of your postings. E.g. he will ignore your questions and ask you to "go away and work out all the possible antidiagonals", or something. Perhaps he will write a piece at the end of your post telling you where YOU are going wrong, and repeat his demand that you answer some ambiguous or irrelevent question. (And yes, with enough persistence he will become abusive.) What he WILL NOT do is respond meaningfully to any requests for mathematical clarification! Later on he'll start another thread using the same unclear terminology, and nothing will have moved on. I think Herc's problem with Cantor's are only sustainable while he is allowed to confuse himself with his ambiguous/contradictory/plain-old-incorrect terminology, but while he will not engage in "meaningful mathematical dialogue" I don't see how anything will change... Mike. > But if, as I increasingly suspect, it's a delusion, then it > will be immune to any kind of disproof. His behaviour here is consistent > with his behaviour when discussing his other delusions - the closer you > get to attacking his core belief, the more abusive he becomes. > > I've never heard of anyone having a delusion about mathematics before. Do you count JSH? He seems to be delusional in a clinical sense. (Unless he's a troll who's just tricking us, in which case I have to say he is very good at it!) I don't know whether Herc is delusional. Like you, I don't think he's a troll. > > Sylvia.
From: George Greene on 22 Jun 2010 14:02
On Jun 22, 2:49 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > > Five-letter insult or not, he's not just opposing Cantor's > > Theorem and he's not just opposing the whole FOL proof machinery: You are just lying. HE IS SO TOO opposing the whole FOL proof machinery. He is fundamentally quantifier dyslexic, OR WOULD BE, IF he would even ACCEPT ENOUGH of the FOL machinery TO DO this with quantifiers. He wants to leap from "there are infinitely many n such that every real is computable to n places" to "every real is computable to infinitely many places". These DO NOT mean the same thing and the latter IS NOT a consequence of the former, BUT HE INSISTS ON CLAIMING THEY ARE EQUIVALENT. > What BS. I have made 3 main valid complaints on transfiniteness No, you have not. > > 1 the powerset proof is essentially > no box contains the box numbers (of boxes) > that don't contain their own box number. That is true, but that is NOT YOUR point. That is RUSSELL'S point. That point PREDATES YOUR BIRTH by over 50 years. That is hardly YOUR point. > > You honestly think this is a great breakthrough? Yes, IT WAS a great breakthrough in logic. It showed that some care had to be taken in formulating comprehension for binary relations. It showed a great MANY DIFFERENT individual truths AT ONCE: NOT ONLY can there NOT be a box "containing all and only" > the box numbers (of boxes) > that don't contain their own box number, but THERE ALSO can't be a barber who shaves all the people who don't shave themselves, or a man who jerks off all the men that don't jerk themselves off, AD NAUSEAM. This is a LOGICAL theorem. It applies EVERYWHERE ALL the time, NOT JUST to numbers and boxes. > > 2 the diag proof is essentially in general form > An AD(n) =/= L(n,n) -> An AD(n) =/= L(n,n) THIS IS BULLSHIT. The anti-diagonal proof IS NOTHING like that in form. THAT form IS CIRCULAR! The fact that you claim the anti-diag proof looks like that just proves that YOU ARE TOO STUPID to see that a is not b ! You are also too damn stupid to even KNOW WHAT THE ARGUMENT of AD is! EVERY square list has an anti-diagonal! The argument of AD(.) IS A SQUARE LIST, NOT a natural number! What IS ACTUALLY the case is that An[ AD(L,n) =/= L(n,n) ]. THAT implies that An[ AD(L) =/= L(n) ]. THAT is what IS ACTUALLY going on, and that is not even "the form of an argument". THAT is just noticing that if ONE list DIFFERS from another at the nth element, THEN THEY ARE NOT THE SAME list! And when this is true for ALL the places on the list, it implies that AD(L) IS NOT *ON* L ! None of this has ANYthing to do with "contains" or "covers" or any other bogus verb that you are stupid ENOUGH to introduce but TOO stupid to define! > it does NOT necessarily generate any new digit sequence You have NOT made this point. IT PROVABLY generates a digit- sequence that IS NOT ON the list. WE HAVE made that point. You just keep ignoring and evading this point. > > IN FACT > > 3 It takes 10^x reals to list every permutation of digits x digits wide Right. > So with infinite reals you can list Every permutation of digits > infinite digits wide. THIS IS BULLSHIT! EVEN IF you were going to MAKE this argument, the argument would be "It takes 10^w reals to list every permuation of digits w wide"!!! THAT, and NOT what YOU said, is what follows from YOUR argument template! If you can NOT EVEN MAKE YOUR OWN argument coherently, if you can JUST SWITCH from "it TAKES x to make y" to "WITH x you can make y", THEN THERE IS NO HOPE!! WITH 40 lines, I can list all the width-3 strings over a 3-digit alphabet, but it does NOT *TAKE* 40; it only TAKES 27!! WITH 23 donuts, I can make a box of a dozen, but it doesn't TAKE 23; it only TAKES 12! Even with YOUR argument, YOUR argument WOULD NOT SAY that "since it takes 10^x lines to list all the strings(over an alphabet of 10 digits) x digits wide, it takes infinity lines to list all the strings infinity digits wide" (which is what you have falsely claimed YOUR argument would say!)! YOUR argument would say that since it takes 10^x liens to list all the digit-strings x digits wide, IT TAKES 10^infinity lines to list all the strings infinity digits wide! THIS IS ACTUALLY *TRUE*!!! Cantor's Theorem is just the proof that 10^infinity IS BIGGER than infinity, JUST LIKE 10^n is bigger than n. > This is a concrete contradiction to the claims > of Cantor's proof. > > It is not me getting it wrong. This is not only you getting Cantor wrong, it's you getting YOUR OWN ARGUMENT wrong!!!!!!! DAMN, You are STUPID!!!!!! |