Cantor Confusion
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From: Tonico on 5 Oct 2006 14:24 mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > > > Why do you think this question be more important or interesting than > > > the other? > > > But the answer is easy: He never writes down the next day, where "next" > > > is a number like "omega". > > > Since the question never mentions a "next day", you answer does > > not address the question. Try again. > > > > Will there exist some pages written by > > X describing the events of some given day of his life, for EVERY > > singled out day of X's life? > > > > > > Note that "omega" is not a day of X's life, so an answer about > > "omega" will not answer the question. > > Since your question does not address my question (the second sentence > was a joke) it remains your turn to try again: > > Is there a day in X's life, such that less than 50,000 years remain to > be written? > > Why do you think this question be less important than yours? And if > not, why do you think that it is meaningful to assert that X could > write about all his days? > > Regards, WM ************************************************************************* If your question was "why is this more important..." , then I already answered this (since I posted the game I address this) in another post. About your question " Is there a day in X's life, such that less than 50,000 years remain to > be written?", the answer appears to be YES, since this guy begins writing his autobiography when his 50,000 years old exactly, so at the end of that day there remains to be written 50,000 years MINUS 1 day...and this relation will remain that way forever, as far as I can see. What I can't see is why is this important? This thinker is designed for people, in particular maths students, to think about the oddities and anti-intuitive shocks one usually gets when getting deep into set theory, infinity and stuff. That's all. Regards Tonio
From: Virgil on 5 Oct 2006 14:25 In article <1160048322.932236.254800(a)b28g2000cwb.googlegroups.com>, "Albrecht" <albstorz(a)gmx.de> wrote: > Virgil schrieb: > > > In article <1160033333.428361.122020(a)h48g2000cwc.googlegroups.com>, > > "Albrecht" <albstorz(a)gmx.de> wrote: > > > > > MoeBlee schrieb: > > > > Give me your axiomatization that is rich enough for ordinary calculus, > > > > and with a mathematical definition of 'constructible', and such that > > > > every real number is constructible. Then we'll talk about that. > > > > > > Do we really need such an axiomatisation? 99% of mathematics was done > > > without it. And was done right. > > > > But 99% is not good enough, in mathematics. > > No, todays math needs 1000%. As it needs infinite^2 and more objects. Actually, it is only A.S.S. who asks for 1000%. Mathematicians would readily accept 100%, but not 99%. > > Best regards > Albrecht S. Storz
From: Virgil on 5 Oct 2006 14:32 In article <1160066063.515422.231130(a)e3g2000cwe.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > > > Why do you think this question be more important or interesting than > > > the other? > > > But the answer is easy: He never writes down the next day, where "next" > > > is a number like "omega". > > > Since the question never mentions a "next day", you answer does > > not address the question. Try again. > > > > Will there exist some pages written by > > X describing the events of some given day of his life, for EVERY > > singled out day of X's life? > > > > > > Note that "omega" is not a day of X's life, so an answer about > > "omega" will not answer the question. > > Since your question does not address my question (the second sentence > was a joke) it remains your turn to try again: > > Is there a day in X's life, such that less than 50,000 years remain to > be written? At any given time there are years worth of days waiting to be written about, but each day will have its day. > Why do you think this question be less important than yours? And if > not, why do you think that it is meaningful to assert that X could > write about all his days? > > Regards, WM Why do you think it is meaningful to assert otherwise? A process which never ends can do an unlimited amount.
From: William Hughes on 5 Oct 2006 15:56 mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > > > Why do you think this question be more important or interesting than > > > the other? > > > But the answer is easy: He never writes down the next day, where "next" > > > is a number like "omega". > > > Since the question never mentions a "next day", you answer does > > not address the question. Try again. > > > > Will there exist some pages written by > > X describing the events of some given day of his life, for EVERY > > singled out day of X's life? > > > > > > Note that "omega" is not a day of X's life, so an answer about > > "omega" will not answer the question. > > Since your question does not address my question (the second sentence > was a joke) it remains your turn to try again: > > Is there a day in X's life, such that less than 50,000 years remain to > be written? No, of course not. This is pretty much the definition of immortal. > Why do you think this question be less important than yours? I don't. What I do think is that the answer to Will there exist some pages written by X describing the events of some given day of his life, for EVERY singled out day of X's life? follows immediately from the answer to the question " Is X immortal". > And if > not, why do you think that it is meaningful to assert that X could > write about all his days? > 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?". The two questions are subtly different. (Pretty much the difference between actual infinity, and potential infinity). I do not draw a distinction between the two questions, however, you do. The problem is that while you can reject "Can X write about all his days?", on the grounds that actual infinity does not exist, you cannot reject "Can X write about every single day?" without also rejecting potential infinity. If you do this you can claim that questions that deal with infinity are meaningless, however, you cannot claim that answers to such questions are wrong. -William Hughes Because X is immortal. There is no "eventually" that he will not reach. So any
From: mueckenh on 6 Oct 2006 04:09
Randy Poe schrieb: > mueckenh(a)rz.fh-augsburg.de wrote: > > Tonico schrieb: > > > > > Han de Bruijn wrote: > > > > Tonico wrote: > > > > > > > > > Han de Bruijn ha escrito: > > > > > > > > > >>Wishful thinking on the part of William Hughes. A simple Google search > > > > >>will reveal that the army of 'sci.math' dissidents is steadily growing. > > > > > > > > > > ************************************************** > > > > > Zaas! Dissidents...from sci.math???? Didn't know somebody already > > > > > formed a political or social or economical or > > > > > whatever-that-isn't-science group called sci.math, and that it already > > > > > has its dissidents! Perhaps Han means people that insist in talking > > > > > about mathematics with some mathematicians from a non-mathematical > > > > > point of view and without knowing mathematics? People that attack > > > > > mathematicians and even mathematics (go figure!) when someone dares to > > > > > point out some mathematical mistake in some nonsense that THEY say is > > > > > correct IN SPITE of evidence in contrary? > > > > > > > > One cannot speak of correct with a mathematics that is a non-discipline > > > > and gives non-discplinary answers to ill-posed questions like this one: > > > > > > > > http://huizen.dto.tudelft.nl/deBruijn/grondig/natural.htm#bv > > > > > > > > Zero balls at noon? Carl Friedrich Gauss would have turned in his grave. > > > > > > > > Han de Bruijn > > > > > > ************************************************** > > > For what we know, I think dead people don't turn in their grave, or > > > anywhere else for that matter. I agree though that the balls-vase-noon > > > is a question ill-posed but with possibilities to be pretty interesting > > > and deep into understanding some aspects of infinity and stuff. > > > I'd rather pose the next thinker. > > > Supose X is a person that never dies, and when he's 50,000 years old > > > he begins writing his autobiography > > > > > > That is not far from the story of Tristram Shandy. > > > > > in a rather peculiar way: every day > > > after his 50,000-th birthday he writes down one day of his life, > > > beginning with his first day of life. The question is: does X write > > > down ALL the days of his life in this autobiography? Pay attention: I > > > am not asking whether there will ever be a book containing all the days > > > of X's life, but rather whether there will exist some pages written by > > > X describing the events of some given day of his life, for EVERY > > > singled out day of X's life...? > > > > Why do you think this question be more important or interesting than > > the other? > > But the answer is easy: He never writes down the next day, where "next" > > is a number like "omega". > > So you think that counting days one at a time beginning > with the 50,000 year, one of those steps will bring you > to "a number like omega"? In other words, the process > of counting finite natural numbers comes to an end? In this case omega is enforced. That is kind of forcing. And when we split the balls escaping from vase A by collecting them in vases B and C at equal shares, then we may speak of the method of forking. Forcing forking shows that the assumption of the existence of omega does not yield consistent results. That has nothing to do with intuition. We see that half of all balls are in B and half are in C at noon. But if C did not exist, then all balls were in B. It is simply ridiculous what kind of logic set theorist must endorse. Regards, WM |