Cantor Confusion
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From: Han de Bruijn on 31 Oct 2006 03:54 Randy Poe wrote: > Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>mueckenh(a)rz.fh-augsburg.de wrote: >> >>>stephen(a)nomail.com schrieb: >>> >>>>Can you describe a continuous version of the problem where each >>>>"unit" of water has a well defined exit time? A key part of >>>>the original problem is that the time at which each ball is >>>>removed is defined and reached. This is crucial to the problem. It is >>>>not just a matter of rates. If you added balls 1-10, then 2-20, >>>>3-30, ... but you removed balls 2,4,6,8, ... then the vase is >>>>not empty at noon, even though the rates of insertions and removals >>>>are the same as in the original problem. So you cannot just >>>>say the rate is 10 in and 1 out and base an answer on that. >>> >>>The answer for any time t *before noon* is independent of the chosen >>>enumeration of the balls. Doesn't that fact make you think a bit >>>deeper? >> >>And add this to the fact that noon and beyond cannot exist >>in this problem. > > I'll ask you the same question I've been asking Tony about > this "existence". > > Did noon exist yesterday? > > Is there anything that prevents me from defining a set > of times t_n, n=1, 2, ... where t_n = 1/n minutes before > noon yesterday? > > As soon as I define those times, does noon yesterday > cease to exist? You may argue as much as you want. But the facts are quite simple. Talking about noon doesn't mean that you "have" noon. If you introduce the notion of "time" in a problem, then that "time" should behave like real (physical) time. And it is a fact that time cannot "flow" through singularities. Thus the fact that the vase explodes means that it's not meaningful to talk about "time" when that happens. Thus there is no way to arrive at noon. A little bit of Physics would be NO Idleness. Just a little bit. You orthodoxies think that "talking" implies "being", while this is not so with Cosmic Disasters, like the Balls in a Vase problem. Han de Bruijn
From: Han de Bruijn on 31 Oct 2006 03:56 David Marcus wrote: > > I guess your definition of "mathematics" is different from mine. Yes. Like your definition of "physics" is different from mine. Han de Bruijn
From: mueckenh on 31 Oct 2006 07:46 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. Regards, WM
From: mueckenh on 31 Oct 2006 07:48 Virgil schrieb: > In article <1162157745.995131.292260(a)k70g2000cwa.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: > > > Dik T. Winter schrieb: > > > > > "positive numbers" with "numbers larger than 0". Because I understand the > > > main domain is Anglo-Saxon mathematics. This is in contradiction to what > > > I did learn at university (0 is both positive and negative). > > > > Really? I never heard of that. Is here anybody who learned that too? It > > would interest me. No polemic intended. > > > > Regards, WM > > French mathematical usage, particularly Bourbaki, uses "positive" > and "strictly positive" where the correspponding English mathematical > usage is, respectively, "non-negative" and "positive". Similarly for > "negative' and "strictly negative" versus "non-positive" and "negative. > Thanks, it is the same in German. Regards, WM
From: mueckenh on 31 Oct 2006 07:51
David Marcus schrieb: > > Do and enjoy your mathematics. I will not disturb you. > > Then why are you posting to sci.math? What do you possibly hope to > achieve? To help those who have not yet decided to study set theory to avoid wasting their time. Regards, WM |