An uncountable countable set
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From: Tony Orlow on 26 Sep 2006 10:40 Han de Bruijn wrote: > Tony Orlow wrote: > >> Han de Bruijn wrote: >>> >>> I may be rude sometimes, but I never get _personal_ by calling somebody >>> an "idiot" or a "crank". Tony's "babbling" translates with Euroglot as >>> "babbelen" in Dutch, which is a word I can use here in the conversation >>> with my collegues without making them very angry (if I say "volgens mij >>> babbel je maar wat"). But, of course, I cannot judge the precise impact >>> of the word in English. Apologies if it is heavier than I thought. >> >> Do you have the saying, "Shallow brooks babble, and still waters run >> deep"? I figured you picked up the usage from this forum, actually. >> It's meant, in English, to mean you aren't making any sense. :) > > I have talked to my collegues and they have told me that "babbling" in > English indeed has a meaning which is somewhat different from "babbelen" > in Dutch. It is more like our "lallen", to be translated in English as > "talking while you are drunk". Is that correct ? Yes, or just with an inherently incoherent mind. > > "Babbelen" in Dutch is more like "having a nice chat". It's not that it > doesn't make any sense, but it's not very deep either. It's more social > than intellectual. Yes, I understand that now. So, maybe, the problem with Mike IS language related.... nahhh. :) > >> Math=Science? > > Definitely, yes! George Boole seemed to think so. I think many have. Would you say that's about equivalent to, "a little physics would be no idleness in mathematics"? I guess you didn't want to talk about having your feet in concrete. ;) > > Han de Bruijn > Tony
From: Tony Orlow on 26 Sep 2006 10:41 Han de Bruijn wrote: > Dik T. Winter wrote: > >> In article <1159211074.494116.142040(a)e3g2000cwe.googlegroups.com> >> Han.deBruijn(a)DTO.TUDelft.NL writes: >> ... >> > I'm still flabbergasted why those difficult proofs as for Fermat's >> Last >> > Theorem or the Poincare Conjecture are not proved then with the full >> > power of modern computers. >> >> Perhaps because computers can only be used to prove finitely many cases >> and that FLT and Poincare are not tangible to be reduced to finitely >> many cases (like 4CT)? > > Has Pythagoras ever been proved automatically? > > Han de Bruijn > I think Pythagorean theorem is a basic fundamental truth about Euclidean space, whether physical or virtual. Has it ever been proved from more fundamental principles? TOny
From: Randy Poe on 26 Sep 2006 10:43 Tony Orlow wrote: > Virgil wrote: > > In article <45189d2a(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > >>> In article <45187409(a)news2.lightlink.com>, > >>> Tony Orlow <tony(a)lightlink.com> wrote: > >> If so, then why do you say "There is no > >> infinite case"? > > > > Because there isn't any. > > There is no noon in the Zeno machine? There's no ball put in at noon in the Zeno machine. All cases, all Zeno balls, are put in before noon. - Randy
From: Randy Poe on 26 Sep 2006 10:45 Tony Orlow wrote: > Han de Bruijn wrote: > > Dik T. Winter wrote: > > > >> In article <1159211074.494116.142040(a)e3g2000cwe.googlegroups.com> > >> Han.deBruijn(a)DTO.TUDelft.NL writes: > >> ... > >> > I'm still flabbergasted why those difficult proofs as for Fermat's > >> Last > >> > Theorem or the Poincare Conjecture are not proved then with the full > >> > power of modern computers. > >> > >> Perhaps because computers can only be used to prove finitely many cases > >> and that FLT and Poincare are not tangible to be reduced to finitely > >> many cases (like 4CT)? > > > > Has Pythagoras ever been proved automatically? > > > > Han de Bruijn > > > > I think Pythagorean theorem is a basic fundamental truth about Euclidean > space, whether physical or virtual. It's a theorem. Note the name. That means it's provable from starting axioms. > Has it ever been proved from more > fundamental principles? Yes. Proofs date back 2500 years. See the page "Pythagorean Theorem and its MANY PROOFS" http://www.cut-the-knot.org/pythagoras/index.shtml - Randy
From: Tony Orlow on 26 Sep 2006 10:51
Han de Bruijn wrote: > Tony Orlow wrote: > >> Virgil wrote: >>> >>> Mathematicians know better. >> >> Define "better". Those that work in various areas of science share a >> notion which defines science. Theories which have no means of >> verification are not science, but philosophy. In mathematics, >> verification really consists of corroboration by other means, >> agreement between different approaches. In science, where you find a >> contradiction with your theory, it needs revision. So, the scientific >> approach to mathematics requires some criterion for universal >> consistency, as measured by the predictions of the various theories >> that comprise it. Where two theories collide, one or both is in error. >> I think that's better. > > Precisely ! In mathematics, there are contradictory approaches, such as > constructivism (Brouwer) against axiomatism (Hilbert). Its practicioners > are asked to be "nice" to each other and to "reconciliate" the different > points of view, which turns out to be a hopeless task. Such a situation > would be unthinkable if mathematics aimed to be a science. > > Han de Bruijn > Well, Han, I'm not sure I agree with the statement that reconciliation is hopeless. Is it hopeless to reconcile the wave nature of elementary entities with their particle nature? No, the same dual natural exists for every object. It's just that, at that scale, the wave nature is as prominent as the particle nature. If the two contradict each other, the universe isn't consistent. But it is. At least science acknowledges that. There is confusion about my "definition" of infinitesimals, because I can see the validity both in nilpotent infinitesimals and in those that are further infinitely divisible. It's a matter of application, the former lending themselves to finite measure and the latter to infinite recursion. It's a matter of scale, where the relatively infinitesimal has no measure. Constructivism and Axiomatism are two sides of a coin. They can be reconciled in larger framework, I think. Tony |