Cantor Confusion
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From: georgie on 4 Oct 2006 08:55 Tonico wrote: > David R Tribble ha escrito: > > > Ross A. Finlayson wrote: > > > Joker, and I've told people this before, please try and ignore Virgil. > > > > Why not ignore Poker Joker? At least Virgil knows set theory. > > > > Virgil, you really ought to refrain from feeding the trolls. > > Their responses are only cluttering up the newsgroup. > ************************************************************** > I agree with David: Poker seems to have taken a step out of reason and > maths and has begun a rather weird and pretty funny, in some cases, > struggle against soundness and intelligence. > I don't know Virgil but he knows some set theory, unlike the Joker, and > any more addressing the joking messages from the joker is just feeding > an already pretty fat troll. > Better to leave the Joker alone; perhaps he'll meet JSH later at some > stage in his trolling life and they'll be happy together thereafter... > Regards > Tonio So you read hundreds of posts because you think poker is a troll but Virgil has added some real mathematics. I think you're sick.
From: Tonico on 4 Oct 2006 09:28 georgie wrote: > Tonico wrote: > > David R Tribble ha escrito: > > > > > Ross A. Finlayson wrote: > > > > Joker, and I've told people this before, please try and ignore Virgil. > > > > > > Why not ignore Poker Joker? At least Virgil knows set theory. > > > > > > Virgil, you really ought to refrain from feeding the trolls. > > > Their responses are only cluttering up the newsgroup. > > ************************************************************** > > I agree with David: Poker seems to have taken a step out of reason and > > maths and has begun a rather weird and pretty funny, in some cases, > > struggle against soundness and intelligence. > > I don't know Virgil but he knows some set theory, unlike the Joker, and > > any more addressing the joking messages from the joker is just feeding > > an already pretty fat troll. > > Better to leave the Joker alone; perhaps he'll meet JSH later at some > > stage in his trolling life and they'll be happy together thereafter... > > Regards > > Tonio > > So you read hundreds of posts because you think poker is a troll > but Virgil has added some real mathematics. I think you're sick. *************************************************************************************** I actually am kindda sick in my back. Thanx for worrying...:) And I do NOT read "hundreds" of post, though you may believe I do. I don't care. And I don't know whether Virgil has added some "real" mathematics (as opossed to nightmared mathematics or what?) or not: he seems to know some set theory, and Poker doesn't. And what hurts you so much about some people calling the joker a troll? Do you feel that the adjective becomes you better than him/her or perhaps he/she is your sweetheart and it makes your heart bleed reading how much fun we make out of his nonsenses? Regards Tonio
From: Han de Bruijn on 4 Oct 2006 10:02 Tonico wrote: > Han de Bruijn wrote: > >>One cannot speak of correct with a mathematics that is a non-discipline >>and gives non-discplinary answers to ill-posed questions like this one: >> >>http://huizen.dto.tudelft.nl/deBruijn/grondig/natural.htm#bv >> >>Zero balls at noon? Carl Friedrich Gauss would have turned in his grave. > > ************************************************** > For what we know, I think dead people don't turn in their grave, or > anywhere else for that matter. It's a litteral translation into English from a Dutch saying. Don't know if it sounds alike in English, though. [ ... well known alternative thinker snipped ... ] > Ps. BTWm abiut the balls-vase matter, I think the best answer is the > one that said that noon, as we know it, is never reached according to > the spirit of the question. That's what I think as well. But it's NOT what mainstream mathematicians think. So beware! And think about _that_. Instead of whining about: >People that attack >mathematicians and even mathematics (go figure!) when someone dares to >point out some mathematical mistake in some nonsense that THEY say is >correct IN SPITE of evidence in contrary? Han de Bruijn
From: Albrecht on 4 Oct 2006 11:28 MoeBlee schrieb: > Albrecht wrote: > > > I will try to explain my claim again: There is only a[n] [anti-]diagonal number > > which is proveable not in the list if there is a real number which is > > build up out of all the real numbers in the list. But for an infinite > > list you can't end the diagonal number. You may have a sequence which > > converge. But you never have a limit. > > Then you're not talking about the reals. The points on a straight line are representations of the reals. Do you think so? With Cantor you have to think that some points on the straight line (to be exact: the absolute majority of them) are not reachable by construction. Should this be a consequence of an useful mathematics? Are the consequences you claim for the Cantor proof really needful? I don't think so. There are many examples in which the systemes break down in extrapolation to infinity. Let's have the sequence of polygones in the circle which numbers of edges run up to infinity. Extrapolate the areas to the limite case and you will get the area of the circle. Isn't it rational to think that the the circle is identic with the limit case of the polygones? Isn't it rational to think that the limit case of the polygones is a polygone with (countable) infinite edges and this edges are identical with (all) the points on the circle line? Concerning Cantors diagonal argument: Can we rational speak about convergence if we don't have a (finite) law which gives us endlessly the converging values? What do you think? Best regards Albrecht S. Storz > We prove that every convergent > sequence of rationals converges to a unique real number, which is the > limit of the sequence. If it converges, then it has a limit. Thus every > countable decimal expansion represents a real number. In particular, > the anti-diagonal of any given countable sequence of denumerable > decimal expansions is a countable decimal expansion and thus represents > a real number. And we prove it does not represent any real number in > the given countable sequence of decimal expansions. > > Argue that you don't like the axioms of set theory, if you like. Argue > that you don't ascribe to the principles of reasoning codified by first > order logic, if you like. But it is not in any way rationally arguable > that the uncountability of the reals is not a theorem of the stated > axioms. And more simply, there is no theory that you have proposed in > which there exists a function from the counting numbers onto the > carrier set of a complete ordered field. > > > Cantor argues that you must not have the limit. > > We must not have the limit of what? And where does Cantor argue this? > Morevover, no matter what Cantor did or did not write, we've moved on > to axiomatic theories that are not at all beholden to Cantor. > > > But with the same idea > > you can e.g. construct a kind of an [anti-]diagonal (natural) number of any > > list of natural numbers. > > So what? If it's a denumerable list of natural numbers, then there is > no anti-diagonal that is a finite sequence or a denumerable that is all > 0's after some position, hence no such anti-diagonal represents a > natural number, since natural numbers are represented only by finite > sequences or by sequences that are all 0's after some position. > > > In > > consequence the set of the natural numbers is uncountable. > > That is incorrect. See above paragraph. > > > You can proof a lot of strange things with the idea of Cantor. > > Many of the ideas originate with Cantor, but the axiomatizations are > not beholden to Cantor. > > > But > > these things are not very useful. > > They axiomatize ordinary calculus used for science and engineering. > Moreover, mathematical logic and set theory were and are very useful in > the development of the digital computer, as you are using such a > digital computer to declare that these are ideas are not very useful. > > MoeBlee
From: Ross A. Finlayson on 4 Oct 2006 11:55
David R Tribble wrote: > Ross A. Finlayson wrote: > > Joker, and I've told people this before, please try and ignore Virgil. > > Why not ignore Poker Joker? At least Virgil knows set theory. > > Virgil, you really ought to refrain from feeding the trolls. > Their responses are only cluttering up the newsgroup. Dave, Tonico, Because Virgil doesn't say anything about set theory, that's why. I ignore Virgil and get along just fine. He apparently ignores me. It's like in a C group, the guy who quotes the standard all the time, and refuses to acknowledge that undefined behavior exists, or that it is implemented in any other way. Actually, Poker Joker here had some interesting comments about definitions and self-referentiality. Maybe he would have stayed on-topic if not badgered. What are we trying to do here anyways? This thread: "Cantor Confusion", on the one hand it's about confusing aspects of transfinite cardinals of Cantorian set theory, generally framed in terms of ZF which is inconsistent, on the other it's "Captain Chaos." It's not much about mutually incompatible points of discourse about theory. So, Dave, what's your opinion about mutually incompatible points of discourse about theory? Can't we all just get along? Where's imagination? Remember when it was said the evens and integers couldn't be compared quantitatively, or there was no way to say in set theory that an infinite proper subset was smaller than the set? That is not the case any more, because people like me took people like Virgil to task for saying that could not be done. If you speak of a universe it's not in ZF, Zermelo-Fraenkel set theory, which is almost Cantorian naive set theory except declared well-founded. Ross |