Cantor Confusion
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From: Franziska Neugebauer on 6 Dec 2006 09:24 Han de Bruijn wrote: > Franziska Neugebauer wrote: > >> Let me summarize: You are mostly off topic. > > Let me summarize: you are mostly not listening. When WM uses > metaphors, for the purpose of convincing you of something, Of what? Of the existence of "false" definitions? Of the "non-existence" of the set of natural numbers? Of the license to swap quantifiers? > these would have been picked up, and interpreted properly by most > normal people. Most "normal" people do at all pick them up. > But not by people with a mathematics (mis-)education, of course, as > I've observed more than once in this newsgroup. Being incapable of > common speech and common sense and ... being proud of it. You know that you are posting to sci.math? F. N. -- xyz
From: Eckard Blumschein on 6 Dec 2006 09:33 On 12/5/2006 10:41 PM, Virgil wrote: > In article <457580FA.1030700(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> That there are more rationals than reals? > > WE do not make any such assumption. I perhaps meant more reals than rationals. I apologize. Dedekind as well as Cantor started from this idea. Cantor even fabricated the notion cardinality in order to quantify the putative difference in size. Considering the rationals a subset of the reals, dull people conclude that there must be more reals than rationals.
From: Eckard Blumschein on 6 Dec 2006 09:50 On 12/5/2006 10:54 PM, Virgil wrote: > 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. Roughly speaking, it just claims that a set is unambiguously determined by its elements. If i recall correctly A=B<-->(A in B and B in A) Perhaps the Delphi oracle provided less possibilities of tweaked interpretation betwixed and between potential and actual infinity.
From: Eckard Blumschein on 6 Dec 2006 10:08 On 12/5/2006 10:59 PM, Virgil wrote: > 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. Just this is fallacious. The reals are continuous like glue. Embedded genuine numbers lost their numerical address. Weyl spoke of a sauce. >> >> >> > Countability >> > /Uncountability are properties of -sets-, not individuals. >> >> Do not reiterate what I know but deny. > > Then do not reiterate your falsehoods Cantor's proof (DA2) of uncountability required numbers of perfectly infinite length. You understand: Such numbers contradict common sense. They are impossible to actually represent. In other words: They are fictions. Now you have to grasp why "sets" of these "elements" are also fictitious and necessarily by no means countable. On the other hand, Cantor was correct in that it does not matter at all how single elements are arranged. One may bring all of then into bijection with the natural numbers. So they are countable even if this counting will never end. Writing very fasr and without proofreading, I cannot guarantee correct command of my English. Sometimes words or letters may be missing or confused. Nevertheless, all these arguments of mine are most likely flawless. >> > 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. You did not refute a single argument of mine.
From: Eckard Blumschein on 6 Dec 2006 10:17
On 12/5/2006 11:01 PM, Virgil wrote: > 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! No. Maybe some mistakable wording gave rise for a false impression. More likely, you and Georg do not understand that there is no number outside an appropriate representation. The abstract concept of numbers must not be misused as to declare rationals and embeded rationals likewise existent. The latter do not obey trichotomy. |