Cantor Confusion
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From: Han.deBruijn on 7 Oct 2006 08:28 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
From: Tonico on 7 Oct 2006 08:31 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". > > Han de Bruijn ****************************** Wrong: whether maths is a science or not, it is NOT grounded on dogma (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. Anyway, I really don't care whether someone thinks maths is or not a science. Tonio
From: Tonico on 7 Oct 2006 08:36 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... Regards Tonio
From: mueckenh on 7 Oct 2006 12:55 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. Regards, WM
From: mueckenh on 7 Oct 2006 12:57
Tonico schrieb: > mueckenh(a)rz.fh-augsburg.de ha escrito: > > > William Hughes schrieb: > > > > > Note the question was very carefully posed so it was not > > > "Can X write about all his days?", but "Can X write about > > > every single day?". > > > > There is the answer 1) There is no day which will not be written. > > There is the answer 2) There is a day which will not be written namely > > the present day. > > > > Both answers contradict each other. > > > > Regards, WM > ******************************************************* > Answer (2) is incorrect, as can easily be proved: the present (this) > day will be written down in 50,000 years more. Q.E.D. Of course you know (?) that the present day is the present day of X, i.e. the day he lives. The present day is a variable. This variable is never set to the value "written" but has always the value "not yet written". Regards, WM |