Cantor Confusion
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From: mueckenh on 7 Oct 2006 12:59 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. Regards, WM
From: Tonico on 7 Oct 2006 13:13 mueckenh(a)rz.fh-augsburg.de ha escrito: > 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. *********************************************** What taxpayers and where have to pay whom for this ""ambiguous nonsense"" (and it of course is neither, but go an convince the barbarians...!)?? Don't you get more shocked by taxes gone for arms expending, corrupt politicians and useless ministeries? Does it REALLY bother you that some rather tiny part of the budget of any developed country goes for universities and an even tinier part reaches the maths deparments?? Have you noticed that the developed, strong, wealthy countries ALWAYS have good math departments in universities? And what is "omega transactions, anyway?!? I don't think that is a meaningdul notion at all...who said it was, why, where and for what? ******************************************************************** > > 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. **************************************************************************** What does the sentence "...the contents of the vase grows in infinity" mean at all?? It sounds just like the christian fundie sentence "I love you in Christ": what does this mean, in the holy name of Woody Allen?!?!? And axioms can yeild whatever they want: that's what they're axioms for! Now that they are consistent, sound axioms is another matter for another discussion. And what are "both sides" of infinity?? The left and right one, or what?! What, in the name of insanity, are you talking about, dude?? ********************************************************************************* > > 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. ********************************************************************************* Man, you do as much sense as some TV preacher do...I wonder....What does "infinity can be calculated" mean? Can you give an example of some mathematician trying to do such a thing, leave alone succeeding? How is that eaten? Do you have to make analysis, algebra, what?!? And then you talk of "infinite nonsense"....oh, yes! Regards Tonio *********************************************** > Regards, WM
From: Tonico on 7 Oct 2006 13:20 mueckenh(a)rz.fh-augsburg.de wrote: > 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". ************************************************************************ Yes...so what?!?!? Just like the sentence "I just lived my last day yesterday" is a variable (?!?!?) that never attains the value "it has been logically said" (not-logically, as I'm sure you wll know, whatever can be said).....hollie mollie, Mueck! Not even Brouwer and his rather weird intuitionist movement could, imfho., have used such nonsense to deffend their ideas... Regards Tonio *************************************************************************** > Regards, WM
From: Virgil on 7 Oct 2006 13:46 In article <1160223586.604282.269450(a)h48g2000cwc.googlegroups.com>, 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". HdB's version of mathematics certainly seems to be grounded in dogma. My mathematics is merely grounded on determining what can be derived from a given set of axioms.
From: Virgil on 7 Oct 2006 13:52
In article <1160224136.694741.319950(a)m7g2000cwm.googlegroups.com>, Han.deBruijn(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. What HdB considers nonsense is only so in his opinion. Others hold the contrary opinion that what HdB declaims as sense is nonsense. The only justification for "no need for further argumentation" is that neither can be convinced by the other. But that does not mean that the issue has been settled in favor of either, merely that each is equally convinced of his own correctness. |