CANTOR DISPROOF <<<<<<<<<<<<<<<<
in [Logic]
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From: |-|ercules on 20 Jun 2010 13:39 "Colin" <colinpoakes(a)hotmail.com> wrote > On Jun 20, 11:45 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> [snip] > > (Yawn.) So, you're spewing your usual jism that there's nothing more > to the real numbers than the computable reals, i.e., that "real > number" and "computable real" are synonyms? Well, Master Debater, > riddle me this: everyone knows the real numbers are closed under the > basic operation of taking the supremum of a bounded sequence. Can you > prove this is true of the computable reals? You have 1000 proofs on real numbers all entrenched together, based on the all new "260". 123 456 789 Diag = 159 Anti-Diag = 260 I'm not writing your axioms for you, and I'm not claiming there are no uncomputable reals at this point, I'm merely stating what fools 99% of mathematicians are. Herc
From: |-|ercules on 20 Jun 2010 13:57 "George Greene" <greeneg(a)email.unc.edu> wrote > Kindly > act like > you understand what is going on. Looks like your subconscious got my message. [Herc] Do I have a point or not? I'm sure you all follow my meaning, but go on full offensive anyway and don't acknowledge what I MEAN. But will it filter through to George's conscious realm. Can he paraphrase my argument per se? He's the only mathematician on usenet who actually does see other perspectives, but his vanity could be an issue acknowledging the point that defeats his Cantor views. Herc
From: Daryl McCullough on 20 Jun 2010 14:08 So what's really going on here, in the minds of several people, is that Herc is a complete ignoramus, and is mathematically incompetent, and the reason he can't accept Cantor's theorem is because he lacks the patience, intelligence, mathematical training, and reasoning ability necessary to follow a simple mathematical proof. In Herc's mind, something very different is happening. Cantor made a bogus proof, and for whatever reason, many mathematicians were bamboozled into believing that it was correct. Ever since then, logic students have been brainwashed into accepting this bogus proof, and are either unable or unwilling to see it as nonsense. They don't want to rock the boat, or they are too timid to question authority, or they are just sheep who believe anything they are told by the "experts" regardless of how nonsensical. (You can replace "Herc" by "WM" here, and you get essentially the same two alternate explanations of what is going on.) People arguing with Herc are in essence attempting to come up with a convincing case that Herc is a complete mathematical incompetent. (And here's the tough part) The argument that Herc is an incompetent has to be convincing to Herc, himself. This is an almost inconsistent requirement. If Herc is incompetent (which he certainly seems to be) then how can you possibly convince HIM of that fact? You can give him arguments, but by assumption, he is incompetent at recognizing valid arguments (if he could recognize valid arguments, he wouldn't be disputing Cantor's proof). My conjecture is that it is completely impossible to make a dent in the convictions of people like Herc and WM. It doesn't help to give a valid argument to people incapable of recognizing valid arguments. -- Daryl McCullough Ithaca, NY
From: |-|ercules on 20 Jun 2010 14:29 > You on the other hand are an unknown geek maths student twerp who recites texts for every > question given to him. I should add, the only reason anyone reads anything you write is because you begin every post with the recognized mantra CANTOR PROVED THAT.... Take that away and you're just another dimwit, ironically you'd be a smarter dimwit if you stopped beginning every post with CANTOR PROVED THAT... but it gets everyone on sci.math listening. Herc
From: George Greene on 20 Jun 2010 15:50
On Jun 20, 2:08 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > My conjecture is that it is completely impossible to make a dent in > the convictions of people like Herc and WM. It doesn't help to give > a valid argument to people incapable of recognizing valid arguments. Valid arguments come IN A WIDE range of DIFFERING degrees of COMPLEXITY OR DIFFICULTY. Herc and WM both ACTUALLY MAKE *simple* valid arguments in arguing their (irrelevant) SUB-points. The goal would basically be to force focus down to something narrow enough to, if not crush into diamond, at least heat the tinder enough to catch a spark. "The anti-diagonal is not on the list" is something that Herc CONCEDES for the finite case. It is sort of unclear why he thinks the infinite case is different. The real failure here is not about "valid arguments" in general but about the 1st-order inference rule of Universal Generalization. When the domain-of-discourse-being-generalized-onto is infinite, SOME people make the mistake of thinking that it is not possible to finish proving the case for THAT MANY instances, not realizing that the whole point is that the ONE instance for which the case has been proved IS ARBITRARY, SO IT DOESN'T MATTER how BIG the domain is. The other problem is a purely natural-language problem about how people think they get to use "all" and "infinitely". Her CONCEDES that the list of all finite digit strings (also) not only "contains", but HAS, AS ELEMENTS, OCCURRING ON IT, every finite prefix of every possible digit-string. But because this holds for infinitely many increasing LENGTHS of prefixes, he THINKS he GETS to SAY that "every finite prefix of every possible digit-string is contained on [whatever] list UP TO INFINITE LENGTH". "Up to infinite length" OBVIOUSLY means something DIFFERENT FROM "up to every finite length". But Herc WILL NOT CONCEDE the difference. Since "contains" is HIS to define (AS, for that matter, is "Up To" -- does "Up To" always CONTAIN the last/limit element? Even when THERE ISN'T one?), there is no final rebuttal UNTIL AFTER he agrees to TRANSLATE "contains" INTO OUR language. But this he will never agree to because the word "infinite" WOULD DISAPPEAR from the locution (it would just be a quantification over a bunch of finite instances), and he would have nothing to equivocate/prevaricate UPON. WM is sort of a separate problem, but he shares the aspect of categorically REFUSING to PHRASE the issue in first-order language with quantifiers, of insisting on doing it in English. The problem IS NOT that EITHER of these people doesn't understand: the problem IS that BOTH of them are HOSTILE to the axiomatic method and first-order logic because THEY KNOW IT REFUTES their cherished belief. So rather than write that way AND RISK LOSING, they keep trying to talk in natural language and to EXPLOIT its imprecision. It is their willingness to do THAT that mandates a harsher response than we have yet been able to deliver. |