Cantor Confusion
in [Math]
|
Prev: Pi berechnen: Ramanujan oder BBP
Next: Group Theory
From: mueckenh on 1 Nov 2006 07:13 David R Tribble schrieb: > mueckenh wrote: > > We cannot approximate sqrt(2) arbitrarily > > close. We can visualize it by the diagonal of a square and we can name > > it. But we cannot approximate it better than to an epsilon of > > 1/10^10^100. It woud be nice if we could, but assuming we can manage > > it, only because otherwise mahematics becomes too difficult, is a bit > > too simple. > > So I guess the natural number > t = 10^(10^10^100) + 10^(10^10^100+1) > can't exist, because it takes 10^(10^10^100)+1 decimal digits to > represent it. (Most of the digits are 0s except for two 1s.) Your guess is wrong. Regards, WM
From: Han de Bruijn on 1 Nov 2006 07:16 Randy Poe wrote: > Han de Bruijn wrote: > >>Virgil wrote: >> >>>In article <f328c$45470fd4$82a1e228$20321(a)news2.tudelft.nl>, >>> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >>> >>>>David Marcus wrote: >>>> >>>>>I guess your definition of "mathematics" is different from mine. >>>> >>>>Yes. Like your definition of "physics" is different from mine. >>> >>>Fair enough. >>> >>>In another post, HdB claimed to have physical evidence that a >>>discontinuity would halt time, or something equally idiotic. >> >>A large mass (as with the balls in a vase close to noon) surely _will_ >>halt time, according to the General Theory of Relativity. > > You are no doubt remembering something you heard about > time inside the Schwarzchild radius of a black hole. > > Point to ponder: Black holes exist in our galaxy. Yet here we > are, with time ticking on regardless. Is it possible you remember > something wrong? That's besides the point. First of all, it has NOT been established that black holes indeed exist in our galaxy. But apart from this, the mass of a black hole is _finite_, while the mass of the balls in a vase becomes _infinite_. So it's much worse than a Black Hole: a Disaster at a Cosmic scale, which cannot be kept in a safe place far away from us. Our clocks would stop ticking _everywhere_, if the thought experiment could become a physical reality. Han de Bruijn
From: Randy Poe on 1 Nov 2006 08:48 Han de Bruijn wrote: > Randy Poe wrote: > > > Han de Bruijn wrote: > > > >>Virgil wrote: > >> > >>>In article <f328c$45470fd4$82a1e228$20321(a)news2.tudelft.nl>, > >>> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>> > >>>>David Marcus wrote: > >>>> > >>>>>I guess your definition of "mathematics" is different from mine. > >>>> > >>>>Yes. Like your definition of "physics" is different from mine. > >>> > >>>Fair enough. > >>> > >>>In another post, HdB claimed to have physical evidence that a > >>>discontinuity would halt time, or something equally idiotic. > >> > >>A large mass (as with the balls in a vase close to noon) surely _will_ > >>halt time, according to the General Theory of Relativity. > > > > You are no doubt remembering something you heard about > > time inside the Schwarzchild radius of a black hole. > > > > Point to ponder: Black holes exist in our galaxy. Yet here we > > are, with time ticking on regardless. Is it possible you remember > > something wrong? > > That's besides the point. First of all, it has NOT been established that > black holes indeed exist in our galaxy. But apart from this, the mass of > a black hole is _finite_, while the mass of the balls in a vase becomes > _infinite_. So it's much worse than a Black Hole: a Disaster at a Cosmic > scale, which cannot be kept in a safe place far away from us. Our clocks > would stop ticking _everywhere_, if the thought experiment could become > a physical reality. But this is not a thought experiment in any sense. It is not governed by physics at all. - Randy
From: stephen on 1 Nov 2006 10:34 Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > Randy Poe wrote: >> Han de Bruijn wrote: >> >>>Virgil wrote: >>> >>>>In article <f328c$45470fd4$82a1e228$20321(a)news2.tudelft.nl>, >>>> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >>>> >>>>>David Marcus wrote: >>>>> >>>>>>I guess your definition of "mathematics" is different from mine. >>>>> >>>>>Yes. Like your definition of "physics" is different from mine. >>>> >>>>Fair enough. >>>> >>>>In another post, HdB claimed to have physical evidence that a >>>>discontinuity would halt time, or something equally idiotic. >>> >>>A large mass (as with the balls in a vase close to noon) surely _will_ >>>halt time, according to the General Theory of Relativity. >> >> You are no doubt remembering something you heard about >> time inside the Schwarzchild radius of a black hole. >> >> Point to ponder: Black holes exist in our galaxy. Yet here we >> are, with time ticking on regardless. Is it possible you remember >> something wrong? > That's besides the point. First of all, it has NOT been established that > black holes indeed exist in our galaxy. But apart from this, the mass of > a black hole is _finite_, while the mass of the balls in a vase becomes > _infinite_. No it does not. At no time is the number of balls in the vase infinite. Remember, the vase is empty at noon. > So it's much worse than a Black Hole: a Disaster at a Cosmic > scale, which cannot be kept in a safe place far away from us. Our clocks > would stop ticking _everywhere_, if the thought experiment could become > a physical reality. Now you are just applying inappropriate math. If the balls and vase were physically realizable, it would involve times less than Planck time, and arbitrarily high speeds, which means it would require new, unknown physics, as none of our current theories say anything about such time intervals or speeds. You cannot apply GR to a situation where it is not applicable. Stephen
From: mueckenh on 1 Nov 2006 13:02
David Marcus schrieb: > mueckenh(a)rz.fh-augsburg.de wrote: > > David Marcus schrieb: > > > > > The set of natural numbers is an infinite set that contains only finite > > > numbers. > > > > Please do not assert over and over again this unsubstantiated nonsense > > (this word means exactly what you think) but give an example, please, > > of a natural number which does not belong to a finite sequence. If you > > cannot do so, then it is obviously unnecessary to consider N as an > > infinite sequence, because all its members belong to finite sequences. > > I didn't say anything about sequences, finite or otherwise. So, your > request is irrelevant to my statement. > The sequence of natural numbers is not comprehensible in ZFC? Neither is the sequence of partial sums of a converging series? Nor are the finite sequences which are called (initial) segments of sequences which are ordered sets. Also the expression "extended sequence" for an uncountable ordered set is new to you? > But, since you clearly haven't studied set theory, how do you > know it is a waste of time? These two lines of yours show: Your study of logic was definitely a waste of time because you neither can recognize facts nor can you draw logic conclusions. 1) I did study set theory. 2) I need not be able to put an egg in order to judge whether it foul. > Considering most of us are discussing modern mathematics, > not Cantor's theory, your statement is not an answer to my question. This is a quotation of Kronecker's, well known to all who studied set theory with a bit of back ground. I supposed 1) you knew that and 2) you were able to understand the meaning of this hint. Sorry that I failed twice. > Don't you think that you should label all your posts as > "NON-STANDARD MATHEMATICS"? Cantor invented omega and defined omega as a whole number. Who changed this standard meaning? Why do you think this meaning was changed? When do you think the contrary meaning became standard? What is the contrary meaning? Do you agree that A n: n < omega is incorrect? If not, why do you complain about non-standard meaning on Cantor's definition of omega as a whole number? Regards, WM |