Obections to Cantor's Theory (Wikipedia article)
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From: Virgil on 28 Jul 2005 03:31 In article <I5YFe.301$Zh.119(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote in message > news:dc9h1k08iu(a)drn.newsguy.com... > > Tony Orlow (aeo6) wrote: > > > >>> Who cares about S_oo? That's not one of the S_n. > > > >>You mean there aren't an infinite number of n in N? > > > > Okay, maybe this will make it clear to you: There is > > exactly 1 natural number that is less than 1: namely 0. > > There is exactly 2 natural numbers that are less than 2: > > namely 0 and 1. There are exactly 3 natural numbers that > > are less than 3: 0, 1, and 2. > > > > You see the pattern? For any n, the number of naturals > > less than n is equal to n. > > > > Now, how many natural numbers are less than infinity? > > I disagree with grouping infinity in with the natural > numbers. That's what Cantorians do. Actually that is precisely what TO does and Cantorians do not do. For Cantorians, infinity is NOT a natural number and no natural number is other than finite. For TO there are infinitely many infinite naturals. So, PJ, who did you say is grouping infinity with naturals?
From: Ross A. Finlayson on 28 Jul 2005 03:35 Virgil, why don't you reply to me anymore? Infinite sets are equivalent. Ross
From: Han de Bruijn on 28 Jul 2005 04:04 Robert Kolker wrote: > Sets are not physical. They are abstract. Search the world over and you > will not find a set. In the real world trees exist but forests do not. > Forests exist in our heads. If I say to you that I can draw a straight line, will you then respond to me that straight lines cannot be drawn, because they are "abstract"? Bob, I know your mantra. And now you know my mantra. Since everything in mainstream mathematics is a set, a mantra is a set. But have you noticed that the intersection of these two mantra's is empty? We have nothing to discuss, Bob, because our universe of discourse is empty. Han de Bruijn
From: Han de Bruijn on 28 Jul 2005 04:47 Randy Poe wrote: > Han de Bruijn wrote: > >>>Randy Poe wrote: >>> >>>>Where do you believe set theory comes up in physics? >>> >>>If you believe that music is physics > > I don't, and I'm more than passing familiar with both. Geez, if we have to talk about competence, credentials and so on, then I'm a philosopher, a physicist, a mathematician, a composer and a poet. >>>... I have an application where set >>>theory is employed > > But that doesn't mean that the sets are real, or that the > chords are really sets. All it means is that you have > created an abstraction of chords in terms of sets. Really? Let's repeat this one: > But that doesn't mean that the sets are real, or that the > chords are really sets. All it means is that you have > created an abstraction of chords in terms of sets. Now tell this to a man in the street and ask him if he understands you. Whatever. It means that you can go back to earth. Because, in the end, you can _hear_ the music. But you cannot go back to earth with _all_ of the set theory in mathematics. And _that_ is the gist of my argument. [ .. snip .. ] Why snip? Because the counter argument is provided by my midi software, more than a thousand times per second, each time it is executed. > By the way, the set description of chords also does not > distinguish inversions, yet inversions are crucial to > "pleasing" chord changes. Duuhh .. How stupid other people than you are, huh Randy? What I've presented in 'sci.math' is a limited description to illustrate just the idea. That's not the way it has to be implemented, of course. Han de Bruijn
From: David Kastrup on 28 Jul 2005 04:53
Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > Randy Poe wrote: > >> Han de Bruijn wrote: >> >>>>Randy Poe wrote: >>>> >>>>>Where do you believe set theory comes up in physics? >>>> >>>>If you believe that music is physics >> I don't, and I'm more than passing familiar with both. > > Geez, if we have to talk about competence, credentials and so on, then > I'm a philosopher, a physicist, a mathematician, a composer and a poet. There is nothing wrong with different skill sets as long as you can keep them apart where they are not related. You can't transfer the openings of chess to checkers. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum |