Galileo's Paradox
in [Math]
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From: Tonico on 5 Dec 2006 02:55 David Marcus wrote: > Eckard Blumschein wrote: > > > Reals, as indirectly defined with DA2, > > Why do you think that the diagonal argument defines the reals? I mean, > you say lots of nonsense, but I don't see where you got this particular > nonsense from. Did you read it in a book? > > -- > David Marcus ***************************************************************** Pssst! Eckie is an engineer (he confessed without any pressure) bored enough to get into trolling/cranking in mathematical stuff: what're the odds he actually read some book in maths, and what are the odds that, if he did, he actually understood it? He doesn't need that to crank: that's the stuff cranking is made of. And as other cranks there are some orbiting semi-cranks around him making an eccho of the big crank's nonsenses: Lester, TO, etc. It can REALLY get boring after some time, but in the meanwhile it can be distracting. Regards Tonio
From: Virgil on 5 Dec 2006 03:12 In article <MPG.1fdee7c0e6fb5e2a9899bd(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > Tony Orlow wrote: > > Virgil wrote: > > > In article <45705ad3(a)news2.lightlink.com>, > > > Tony Orlow <tony(a)lightlink.com> wrote: > > > > > >> Huh! So, what happens if I declare a number, Big'un, and say that that > > >> is the number of reals in (0,1]? What if I say the real line is > > >> homogeneous, so every unit interval contains the same number of points? > > >> And then, what if I say the positive number line is going to include > > >> Big'un such unit intervals, so it has Big'un^2 reals up to Big'un? Does > > >> the universe collapse, or all tautologies suddenly become false? > > > > > > As long as it is only TO playing his silly games, nobody much cares. > > > > > > If TO were ever to produce anything like a coherent system with actual > > > proofs, we might actually have to pay some attention. > > > > Of course, that would be nice, to get some attention around here, > > especially from Virgil. But, he never pays me no mind. He hardly > > responds to anything I say. > > Virgil obviously meant mathematical attention as opposed to crank > attention. Amen!
From: Eckard Blumschein on 5 Dec 2006 04:32 Let's rank Tonico outside but David Marcus still inside mathematics. On 12/5/2006 8:55 AM, Tonico wrote: > David Marcus wrote: >> Eckard Blumschein wrote: >> >> > Reals, as indirectly defined with DA2, >> >> Why do you think that the diagonal argument defines the reals? You all know that DA2 shows by contradiction that real numbers are uncountable. I carefully read how Cantor made sure that the numbers under test are real numbers. He did not use Dedekind cuts, nested intervals or anything else. He assumed numbers with actually indefinitely much rather than many e.g. decimals behind the decimal point. Strictly speaking, he did not immediately show that the reals are uncountable but that these representation like never ending decimals is uncountable. Being uncountable is the common property of these numbers under test. To my knowledge, sofar nobody was able to show that the numbers allegedly defined by Dedekind's cut or nested intervals are uncountable. If we need the notion real numbers at all, then in connetion with the common property to be uncountable. You might wondwer that there is no chance to define the reals at will. Cantor made a false promise when he said the essence of mathematics just resides within its fredom. Do you still not yet understand why DA2 lets no room as to define the reals accordingly? The decisive difference between DA2 and all presentlxy preferred definitions is a categorical one: Actually indefinitely much is a fiction. Real numbers have to be fictitious. I mean, >> you say lots of nonsense, in the sense it did not yet make sense to you. but I don't see where you got this particular >> nonsense from. Did you read it in a book? I read several original papers by Cantor. The rest is reasoning. >> >> -- >> David Marcus > ***************************************************************** > Pssst! Eckie is an engineer (he confessed without any pressure) bored > enough to get into trolling/cranking in mathematical stuff: what're the > odds he actually read some book in maths, and what are the odds that, > if he did, he actually understood it? > He doesn't need that to crank: that's the stuff cranking is made of. > And as other cranks there are some orbiting semi-cranks around him > making an eccho of the big crank's nonsenses: Lester, TO, etc. > It can REALLY get boring after some time, but in the meanwhile it can > be distracting. > Regards > Tonio >
From: Eckard Blumschein on 5 Dec 2006 04:35 On 12/5/2006 8:24 AM, David Marcus wrote: > Eckard Blumschein wrote: > >> Reals, as indirectly defined with DA2, > > Why do you think that the diagonal argument defines the reals? I mean, > you say lots of nonsense, but I don't see where you got this particular > nonsense from. Did you read it in a book? Please find my answer to this question in my reply to Tonio below. >
From: Tonico on 5 Dec 2006 06:50
Eckard Blumschein ha escrito: > Let's rank Tonico outside but David Marcus still inside mathematics. ****************************************************** Zas! The engineer that-particularly-sucks-in-maths ranks me, a mathematician, out of mathematics....hehe...how cranky can you get? Oh well: apparently a lot. ****************************************************** >> but I don't see where you got this particular > >> nonsense from. Did you read it in a book? > > I read several original papers by Cantor. The rest is reasoning. ****************************************************** Reading is not the same as understanding, and staring blank at a paper, or knowing how to type and posting in a maths group, is not the same as reasoning. Eckard is terribly ill-educated in maths, but he believes that his lack of education and of understanding advanced maths is due to the fact that great mathematicians of the past, like Dedekind, Cantor, Hilbert, Fraenkel, etc. were wrong...because, of course, he can NOT be wrong. The grudge Eckie has against Dedekind is specially interesting and, for him, apparently painful: Eckie seems to believe (BELIEVE, as in religious faith) not only that Dedekiind was dead wrong, but also that Dedekind was evil and deceiful on purpose. And I even think that Eckie believes Dedekind was that evil only to annoy him (Eckie)...! This is what could be called, imo, anachronical cranking: this poor engineer guy believes that a great mathematician of the past did something wrong ON PURPOSE just to bother him. Well, if it weren't hilarious it'd be sad. Regards Tonio |