Cantor Confusion
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From: William Hughes on 7 Oct 2006 14:03 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". > Ok. Let's call a day a "numbered day", if we are able to associate the day with a specific natural number. So day 5,341,134,322, is a numbered day, but the present day is not a numbered day. The question is now: "Can X write about each numbered day?" - William Hughes
From: Virgil on 7 Oct 2006 14:05 In article <1160240157.508221.220360(a)k70g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > 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. Absolutely false. Before any balls are put in the vase, it is empty, and after al balls have been removed from the vase it is equally empty. It is only between these time that there are any balls in the vase at all. > And of course, this is also valid too for noon, if > omega transactions is a meaningful notion at all. What in blazes are "omega transactions"? > To assert that at > noon (finished infinity, actualized transfinity) the vase is empty is > not counter-intuitive but it stupid. But nowhere near as stupid as claiming that balls that have been removed are still there. > > > 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. "Mueckenh" presumes some sort of "continuity" at noon, but the whole process is discontinuous at each time of change. The function which counts balls in the vase as a function of time jumps discontinuously when any ball is inserted and also when any ball is removed. Since noon is a condensation point of such discontiuities, it is bootless to insist that it be a point of psuedocontinuity such as "Mueckenh" claims. > > > Otherwise just go and be an engineer and say An engineer cannot put balls into or take balls out of a vase instantaneously, nor can he put infinitely many balls into a vase at all, so that an engineering is irrelevant. > > 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. "Mueckenh" is certainly hopeless.
From: Virgil on 7 Oct 2006 14:10 In article <1160240267.396485.153440(a)c28g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Tonico schrieb: > > 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". Then "the present day plus 50,000 years" is equally a variable and is the day on which the events of "the present day" will finally "be written down".
From: Virgil on 7 Oct 2006 14:11 In article <1160240378.412923.220310(a)e3g2000cwe.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > David Marcus schrieb: > > > What do you mean by "cover"? > > A covers B if A has at least as many bars as B. Then New York "covers" Chicago.
From: Tonico on 7 Oct 2006 14:30
Virgil ha escrito: > In article <1160240378.412923.220310(a)e3g2000cwe.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: > > > David Marcus schrieb: > > > > > > What do you mean by "cover"? > > > > A covers B if A has at least as many bars as B. > > Then New York "covers" Chicago. ***************************************************8 LOL! This made me laugh....damn! Thanx Regards Tonio |