Cantor Confusion
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From: Virgil on 5 Dec 2006 16:41 In article <457580FA.1030700(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/5/2006 12:34 AM, Virgil wrote: > > In article <45745F0A.2000408(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > > >> On 12/1/2006 9:42 PM, Virgil wrote: > >> > In article <45706268.1020005(a)et.uni-magdeburg.de>, > >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> > > >> >> On 12/1/2006 1:37 AM, Dik T. Winter wrote: > >> >> > In article <456EEA86.20001(a)et.uni-magdeburg.de> Eckard Blumschein > >> > > >> >> > Oh, for once, try to talk mathematics. By the axiom of infinity the > >> >> > set of all naturals is neither hypothetical nor fictitious. > >> >> > >> >> This axiom combines flawless Archimedean reasoning with an at least > >> >> questionable replacement of the notion number by the notion set. > >> > > >> > When EB presents a completed axiom system from which he can generate > >> > mathematics, or at least arithmetic, he may join the lists, but until > >> > then he is merely a spectator at mathematics, and not competent to be a > >> > judge. > >> > >> At least, a spectator is not blind. > > > > A spectator who chooses not to see what is there to be seen, as WM keeps > > doing, is no better off that if he were blind. > > Why do you mean is to be seen? EB chooses to see only what he wants to see, without admitting the hidden assumptions he makes to justify what he wants to see. Set theorists at least have the virtue of stating their assumptions up front as an axiom system. > That there are more rationals than reals? WE do not make any such assumption. > I see it, see it a fallacy behind it, see the consequences of this > fallacy carefully hidden behind the huge junk of set theory und hope for > more intelligent youngsters. The more intelligent they are, the less susceptible to EB's anti-logic.
From: Virgil on 5 Dec 2006 16:54 In article <4575A562.60602(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > Blissful ignorance of mathematicians does not utter complains if the > axiom of (possibly infinite) extensionality claims the existence of a > set which has to include all of its elements. EB should read what axioms of extensionality actually says before pontificating.
From: Virgil on 5 Dec 2006 16:59 In article <4575B447.50208(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/5/2006 2:13 PM, Bob Kolker wrote: > > Eckard Blumschein wrote: > >> an exact numerical representation available. Kronecker said, they are no > >> numbers at all. Since the properties of the reals have to be the same as > >> these of the irrationals, all reals must necessarily also be uncountable > >> fictions. > > > > For the latest time. Uncountability is a property of sets, not > > individual numbers. > > I know this widespread view. > > > There is no such thing as an uncountable real > > number. > > Real numbers according to DA2 are uncountable altogether. People like > you will not grasp that. Not a single real number is countable. > > > Nor is there any such thing as a countable integer. > > Every single integer is a countable element. Since the set of integers is a subset of the set of reals, every integer is a real in any real set theory, whatever Eb may claim. > > > > Countability > > /Uncountability are properties of -sets-, not individuals. > > Do not reiterate what I know but deny. Then do not reiterate your falsehoods > > > > > You have been told this on several occassions and you apparently are too > > stupid to learn it. > > You should try and refute. We have refuted it many times, but those who choose not to see remain blind.
From: Virgil on 5 Dec 2006 17:01 In article <4575B6E1.4010505(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > I consider my ideas still flawless. An attitude of fools.
From: Virgil on 5 Dec 2006 17:01
In article <4575B727.6070006(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/5/2006 3:36 PM, Georg Kreyerhoff wrote: > > Eckard Blumschein schrieb: > > > >> Do not confuse Cantor's virtue of belief in god given sets with my power > >> of abstraction. > > > > Your power of abstraction is nonexistant. You're not even able to > > distinguish > > between representations of numbers and the abstract concept of numbers. > > > > Georg > > Really? Really! |