Cantor Confusion
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From: Lester Zick on 7 Dec 2006 13:18 On Thu, 07 Dec 2006 06:48:40 -0500, Bob Kolker <nowhere(a)nowhere.com> wrote: >mueckenh(a)rz.fh-augsburg.de wrote: > >> >> >> Those who pretend to be able of knowing every integer and, therefore, >> to imagine the whole actually infinite set. > >If there were an integer I could not imagine, there would have to be a >least such integer. Well, it isn't 0 or 1. So the least integer I could >not image has a predecessor. But I can imagine it. I could also imagine >adding one to it. > >Contradiction. Also sprach philosopher Bob. ~v~~
From: Mark Nudelman on 7 Dec 2006 13:43 On 12/7/2006 3:15 AM, Eckard Blumschein wrote: > Just try and refute: > > Reals according to DA2 are fictitious > Reals according to DA2 are fictitious > With fictitious I meant: They must not have a directly approachable > numerical address. This was the basis for the 2nd DA by Cantor afer an > idea by Emil du Bois-Raymond. > > Good luck > Can you define what you mean by a "directly approachable numerical address"? Do you mean that SOME reals don't have such an address, or that NONE of them have such an address? Is "sqrt(2)" a "directly approachable numerical address"? If you're saying that some reals do not have a finite decimal representation, that's true, but so what? Why does that make them any more "fictitious" than the integers? --Mark
From: MoeBlee on 7 Dec 2006 14:40 mueckenh(a)rz.fh-augsburg.de wrote: > Bob Kolker schrieb: > > Also the set of natural numbers has a > > cardinality greater than the cardinality of any set {2*1, 2*2 ..., 2*n} > > for any integer n. Since the set of integers is equinumerous with the > > set of even integers (by way of the mapping n<->2*n) > > They are not equinumerous by the way of mapping n <--> n. AGAIN you show that you don't understand even the basics of this subject. It doesn't even make SENSE to say that two sets are not equinumerous by a certain mapping. 'x is equinumerous with y' is DEFINED as 'there exists a bijection between x and y'. That a certain function is not a bijection between x and y does not refute that there is some other function that IS a bijection between x and y. Sheesh! MoeBlee
From: Virgil on 7 Dec 2006 14:47 In article <4577F0AD.7070802(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > I call such numbers > genuine numbers. Absent mathematical definitions of "genuine" versus "fictional", they are both mathematically mere goobledegook nonsense words. > Moreover, rational numbers loose > their property of being countable if they are embedded into the > continuum. Then according to EB, finite subsets of the reals are uncountable. Eb's misuse of mathematical terms is.unaccountable > At least there is no possiblity to > decide inside the genuine continuum whether a fictitious "element" How can a "genuine" continuum be made up entirely of "fictitious" elements? > The primary continuum is strictly speaking amorph. > There is no structure available inside this continuum. Then it is not a mathematical object at all, as every mathematical continuum has a good deal of internal structure. Such non-mathematical notions are of no interest within mathematics. Let us not hear about them further! EB's anti-mathematical rants create more smoke than light.
From: MoeBlee on 7 Dec 2006 14:49
mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > Please clarify a point of nomenclature. > > Do you consider a potentially infinite > > set containing only finite elements > > (e.g. the natural numbers) to be: > > > > 1. a set ? > > 2. a finite set? > > It is neither an actually infinite set nor is it a set in the sense of > set theory. > I call it a set, because "set" is a handsome word. I call it an infinte > set, because it is not a finite set. But if I talk to you about that, > you cannot understand, because you can only think in the notions of set > theory. No, you can't talk about it because you don't HAVE a theory. If you had a theory that were not set theory, then that in itself would not prohibit people who understand set theory from also understanding your theory. But you dont' have a theory, so the whole matter is nugatory anyway. MoeBlee |