Cantor Confusion
in [Math]
|
Prev: Pi berechnen: Ramanujan oder BBP
Next: Group Theory
From: mueckenh on 7 Oct 2006 15:28 Tonico schrieb: > Han.deBru...(a)DTO.TUDelft.NL wrote: > > Dik T. Winter schreef: > > > > > Also when somebody writes a bold statement that the axiom of infinity > > > leads to nonsense, that is just opinion, and nothing more than that. > > > > Wherefore by their fruits ye shall know them (Matthew 7:20). > > For example the Balls in a Vase problem clearly shows what nonsense is > > the consequence of contemporary mathematical thinking. There is no need > > for further argumentation. > > > > Han de Bruijn > *********************************************************** > I'll be candorously innocent...Han, please: what nonsense is that > you're talking about related to the vase balls problem, and how does it > come from "contemporary mathematical thinking"? And what would this > "contemporary mathematical thinking" be? > I wonder whether I'll get a response... You got it several times already. According to the axiom of infinity the set of all natural numbers does exist. And with it the following statements are true: 1) Before noon every ball comes out of the vase. At noon the vase is empty. 2) Before and at noon there are more balls in the vase than have come out. Regards, WM
From: David Marcus on 7 Oct 2006 15:44 mueckenh(a)rz.fh-augsburg.de wrote: > > David Marcus schrieb: > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > Hi, Dik, > > > > > > I would like to publish our result to the mathematicians of this group > > > in order to show what they really are believing if they believe in set > > > theory. > > > > > > There is an infinite sequence S of units, denoted by S = III... > > > > > > This sequence is covered up to any position n (included) by the finite > > > sequences > > > I > > > II > > > III > > > ... > > > > What do you mean by "cover"? > > A covers B if A has at least as many bars as B. A and B are unary > representations of numbers. > > Example: A = III covers I and II and III but not IIII. > > > But it is impossible to cover every position of S. > > > So: S is covered up to every position, but it is not possible to cover > > > every position. So, your conclusion is that no finite sequence of I's will cover S. Correct? Is this your entire theorem or is there more to the conclusion? -- David Marcus
From: Han.deBruijn on 7 Oct 2006 16:15 Tonico wrote: > Han.deBru...(a)DTO.TUDelft.NL wrote: > > Dik T. Winter schreef: > > > > > Also when somebody writes a bold statement that the axiom of infinity > > > leads to nonsense, that is just opinion, and nothing more than that. > > > > Wherefore by their fruits ye shall know them (Matthew 7:20). > > For example the Balls in a Vase problem clearly shows what nonsense is > > the consequence of contemporary mathematical thinking. There is no need > > for further argumentation. > > > *********************************************************** > I'll be candorously innocent...Han, please: what nonsense is that > you're talking about related to the vase balls problem, and how does it > come from "contemporary mathematical thinking"? Please read this carefully, Tonico, and make up your mind: http://huizen.dto.tudelft.nl/deBruijn/grondig/natural.htm#bv > And what would this "contemporary mathematical thinking" be? Different from the mathematical thinking at the time e.g. Gauss was still alive: http://www.mathacademy.com/pr/minitext/infinity/ According to this web page, Gauss has said: > As to your proof, I must protest most vehemently against your use > of the infinite as something consumated, as this is never permitted > in mathematics. The infinite is but a figure of speech . . . . The remainder of this web page ("Cantorian mathematics") is still a hot topic in many of the 'sci.math' threads. Mainstream mathematics accepts completed infinities. But many others (e.g. myself) do not. > I wonder whether I'll get a response... You're quite welcome. Han de Bruijn
From: Han.deBruijn on 7 Oct 2006 16:28 Tonico wrote: > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > Tonico wrotef: > > > > > Maths, just like the other sciences, isn't grounded on dogma, and > > > people forwarding REASONABLE, well-based objections, opinions or ideas > > > on whatever are always welcome. > > > > _There_ is your problem! Ask Virgil, and the other mathematicians here: > > > > MATHEMATICS IS _NOT_ A SCIENCE > > > > And therefore there is NO guarantee that it "isn't grounded on dogma". > > > ****************************** > Wrong: whether maths is a science or not, it is NOT grounded on dogma There are several forms of mathematics. Some of them are NOT grounded on dogma (presumably the forms you are aware of), but others certainly are. They call it not dogmas but axioms. There is nothing wrong with axioms as such. But there CAN BE something wrong with axioms that come out of thin air and are contradictory to physical experience. Such as axioms which embody the idea that completed infinities could possibly exist. > (or better: mention one dogma of mathematics). > About maths being or not a (natural) science: I think that may depend > on what definition we use for "natural science". Maths doesn't require > labs, observation of physical phenomena or testing of results again and > again, just as chemistry, physics or biology may need, but maybe not > only that is what makes a science according to other definitions. How about computers? Aren't they the labs of modern mathematics? > Anyway, I really don't care whether someone thinks maths is or not a > science. Because in your view, mathematics IS a science. No? According to my personal opinion, mathematics _should be_ a science. Han de Bruijn
From: Han.deBruijn on 7 Oct 2006 16:34
mueckenh(a)rz.fh-augsburg.de schreef: > Tonico schrieb: > > > Nonsense. This is a mathematical question posed by mathematicians to > > mathematics students, so we abide by mathematics rules and not by our > > whims. > > Given the information of that Tristram Shandy story, the answer is > > pretty simple and even very easy to prove: EVERY single day of his life > > will be written down, even if it'd take 1 millions years to Tristram to > > write every day, and not merely one year. Does this shock your > > intuition? > > No, but what shocks me is that the tax payer has to pay money for such > ambiguous nonsense. The story of Tristram Shandy is similar to the > vase, even though the vase is more clear about limits. We know, not by > intuition, but by logic, that the vase at any time contains more balls > than have escaped. And of course, this is also valid too for noon, if > omega transactions is a meaningful notion at all. To assert that at > noon (finished infinity, actualized transfinity) the vase is empty is > not counter-intuitive but it stupid. > > > Good, that's how this is suposed to work: you can follow > > your intuition in maths, but be sure to apply LOGIC, AXIOMS and reason > > to confirm your intuition. > > Apply simply the knowledge that the contents of the vase grows, in > infinity. No axiom is powerful enough to yield the contrary. This story > only tells us that, if both sides of infinity are considered > 1) Before noon every ball comes out of the vase > 2) Before and at noon there are more balls in the vase than have come > out > then the axioms yield a contradiction. > > > Otherwise just go and be an engineer and say > > to all you know maths....**sigh**. > > You write "More than 99% of his life remain unwritten", and three words > > later YOU ALSO write "Even if he lives forever"...!!!! If you can't see > > the HUGE nonsense this is, EVEN from the standpoint of your rather > > bizarre opinions about infinity and stuff, then all is hopeless. > > It is nonsense, but it is the truth if infinity can be calculated. I > said it merely to show that actual infinity is not only a huge nonsens > but rather an infinite nonsense. And when you're debating with me (HdB). I'm on Mueckenheim's side in these matters. Han de Bruijn |