Cantor Confusion
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From: David R Tribble on 4 Oct 2006 16:53 Ross A. Finlayson wrote: > 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? They can't all be right. > Can't we all just get along? If you mean "can't we we all behave like adults", I would hope so. > Where's imagination? Indeed.
From: Virgil on 4 Oct 2006 16:57 In article <1159994829.764966.169170(a)i3g2000cwc.googlegroups.com>, "georgie" <geo_cant(a)yahoo.com> wrote: > Tonico wrote: > > georgie wrote: > > > 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 > > I can't recall seeing PJ's remarks all over the NG. Virgil's worthless > statements seem to be everywhere. If "georgie" doesn't like my posts, why doesn't he/she/it killfile them?
From: David R Tribble on 4 Oct 2006 17:08 Albrecht wrote: >> 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? > guenther vonKnakspot wrote: > Mathematics does not have to be useful. As it is, however, it is quite > useful and that is exactly because it is as it is, not in spite of that > fact. But it wouldn't be as soon as it was crippled in order to > accomodate dimwits as yourself. And that is the main problem with your > kind. You fail to understand counterintuitive concepts and demand that > they be banned. And on the flip side, a casual perusal of this newsgroup shows several posters with "novel" concepts, and in response to these, an overwhelming number of requests for proofs of those concepts. But no meaningful proofs or definitions are ever given. So on the one hand, we've got those people who feel that proven and accepted but "counterintuitive" concepts should be eliminated, but on the other hand those same people are more than happy to present their own concepts, unproven and ill-defined, as somehow "better".
From: William Hughes on 4 Oct 2006 18:45 Han de Bruijn wrote: > Albrecht wrote: > > > William Hughes wrote: > > > >>If you do not allow "completed infinite sets", then the meat > >>of Cantor's proof (the cardinality of the reals is greater than > >>that of the integers) cannot be done > >>So, everyone who finds your "contradictions" to be convincing > >>will find Cantor rather trivial. > > > > Any proof which shows that infinity is incomprehensible isn't trivial. > > It must be a proof, which is working on the limit of the knowable. > > LIMIT is the keyword. All true knowledge about the infinite starts with > finite things. The deep reason behind this is that infinity can never be > observed in nature. Infinity is just an idealization of the finite which > helps us to deal with "large quantities". That's why limits are the one > and only sensible road to infinity. > > >>However, as far as I can see, 'everyone who finds your > >>"contradictions" to be convincing', is a set with at most > >>one element. > > > > Maybe. > > Wishful thinking on the part of William Hughes. A simple Google search > will reveal that the army of 'sci.math' dissidents is steadily growing. > There are certainly a lot of dissidents on sci.math. However, besides the fact that standard mathematics is wrong, they agree on little. Even when they agree in result (as in this case) they tend to have different reasons. My comment was based on the fact that I have never seen a posting supporting Albrechts reasoning. This does not of course mean that no one find his reasoning convincing. Do you find Albrechts "contradictions" convincing? - William Hughes
From: Ross A. Finlayson on 4 Oct 2006 21:30
David R Tribble wrote: > Ross A. Finlayson wrote: > > 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? > > They can't all be right. > > > Can't we all just get along? > > If you mean "can't we we all behave like adults", I would hope so. > > > Where's imagination? > > Indeed. Well, they might. Consider Euclidean and non-Euclidean geometry. In Euclidean geometry you can't make non-Euclidean forms, and in non-Euclidean geometry you can't not have some non-Euclidean forms, Riemannian or Lobachevskyan or Minkowskian and etc. Before they could be called mutually incompatible, instead of uh, interchangeable, there would have to be establishment of a somewhat stricter meaning than probably either party would themselves have. Geometry can go right out negating the axioms and having combinations of each possible axiom set, in defining anti-points and etc. I made the reference about C because you're an expert on the standard and know there's undefined behavior, and actually probably what it would be also, Dave, and they don't suffer off-topic posts gladly on comp.lang.c. See, Dave, now you'll support the status quo, I appreciate that. It helps to understand that the mathematical status quo represents quite the body of mathematical practice, and what that is. I support the status quo whenever I feel like it. You'll notice these mathematical foundations get into all these kinds of mathematics. You don't see me tearing down the status quo, do you? That's why it feels so good to (think that you) have found something wrong with it. I'm in it for the chicks, money, and a research institution named after me. It helps that I don't bliss out every time I figure something out, so I was impressed when Poker Joker wrote something that some few days earlier I had been considering, which I rarely do, and he formulated what I would have wanted to say in an eloquent way. So, sci.math is easily productive, and it happens to be the place on the whole Internet where all the Cantor talk has dropped. So what? Ross Finlayson's Null Axiom Theory, who cares? It's obvious, what's the problem? It's the Theory of Everything. I say that, what you call, candidly. Captain Chaos, indeed. Ross |