An uncountable countable set
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From: Han de Bruijn on 27 Sep 2006 03:37 MoeBlee wrote: > Tony Orlow wrote: > >>Constructivism and Axiomatism are two sides of a coin. They can be >>reconciled in larger framework, I think. > > I don't know what your definition of 'axiomatism' is, but there are > axiomatic systems for constructive mathematics. True. And I consider that as a distortion of contructivism. Abandon Axioms and Acquire an Abacus (: Mueckenheim ?) Han de Bruijn
From: MoeBlee on 27 Sep 2006 09:47 Han de Bruijn wrote: > MoeBlee wrote: > > > Tony Orlow wrote: > > > >>Constructivism and Axiomatism are two sides of a coin. They can be > >>reconciled in larger framework, I think. > > > > I don't know what your definition of 'axiomatism' is, but there are > > axiomatic systems for constructive mathematics. > > True. And I consider that as a distortion of contructivism. Let's suppose axiomatization conflicts with constructivism. What exactly do you see that conflict to be? And what do you find so important in constructivism that upholding it is more important than the objectivity of axiomatization? MoeBlee
From: Tony Orlow on 27 Sep 2006 10:18 Randy Poe wrote: > 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 > Oh. Thanks. I'll take a look. Heh.
From: Tony Orlow on 27 Sep 2006 10:21 Randy Poe wrote: > Tony Orlow wrote: >> Randy Poe wrote: >>> 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 >>> >> At any time finitely before noon, only a finite number of balls have >> been processed. Do you disagree? > > I agree. > >> Are you suggesting that the vase fills >> at some *infinitesimal* amount of time before noon? > > No. There is no time before noon when the vase is full. > Let t be any time before noon. Infinitely many balls > will be inserted into the vase after t, but before noon. > >> How does that differ, in your view, from being *at* noon? > > Well since I also don't say "it fills at an infinitesimal > time before noon", there is no need to distinguish > one nonsensical statement from the other. > > - Randy > But, you do say it fills, or empties, right? And, at the same time you say it does not do so at noon, nor does it do so before noon. When does this occur? Tony
From: Tony Orlow on 27 Sep 2006 10:22
Virgil wrote: > In article <6e5c2$4518da26$82a1e228$6365(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> 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 ? >> >> "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. >> >>> Math=Science? >> Definitely, yes! > > Only if science is a subset of mathematics. There is no science without mathematics, if that's what you mean. Tony |