Cantor Confusion
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From: Eckard Blumschein on 6 Dec 2006 10:21 On 12/5/2006 11:04 PM, Virgil wrote: > In article <4575B9F3.7080107(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> >> Reals according to DA2 are fictitious > > No one mathematically competent who is at all familiar with Cantor's 2nd > proof finds any such thing falsehoods in it. > > It is EB who is fictitious. Set theorist may wish this. No my arguments are real and unrefuted. There is not just the so called 4th possibility. I indeed applies.
From: mueckenh on 6 Dec 2006 10:22 Franziska Neugebauer schrieb: > mueckenh(a)rz.fh-augsburg.de wrote: > > > Virgil schrieb: > [...] > >> What limits thought to only the accessible part of the universe? > > > > The fact that any brain consists of not more than this limited part of > > the universe. > > > > And the fact that the power set of your neurons and ideas > > How do you know that there is an inaccessible, unlimited part of the > universe beyond this accissible one? No idea. > If you don't: Do you think it is > meaningful at all to distinguish the accessible from the inaccessible? Yes, of course. It is meaningful in order stop the agument that there may be sme infinity. > > > and other contents of our brain is a finite set. > > No single "content of our brain" is a set Z-set theoretically. > "Contents of our brain" is the subject of neuro sciences not of > mathematics. Hence you are off topic. A very short-sighted opinion. > > > And the power set of this set is a finite set too. And so on, in > > infinity ... (potential infinity , of course) > > You still have not yet understood the concept of inifinite sets. I have understood the concept and its failure. (That is the parallel between those who have not yet arrived and those who have already left: Both are not there.) Regards, WM
From: Han de Bruijn on 6 Dec 2006 10:26 Franziska Neugebauer wrote: > Han de Bruijn wrote: > >>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? Yeah, so what? There exist also _well_-educated mathematicians. Which means that they have absorbed more of the world than just mathematics. And they do not think that Set Theory is the panacea for all diseases. Han de Bruijn
From: mueckenh on 6 Dec 2006 10:29 Franziska Neugebauer schrieb: > mueckenh(a)rz.fh-augsburg.de wrote: > > > Dik T. Winter schrieb: > >> > Everybody knows what the number of ther EC states is. > [...] > > The number of EC states is "the number of EC states". > > This is hardly a definition. > > > It is simply a notion which can be equal to a natural number. > > Which may _evaluate_ to a number. No. It evaluates to a number as little as 6 evaluates to a number. It *is* a number, though not a fixed number. That is a matter of definition of the word "number". > Without explicitly or implicitly > providing a context (year) there is no definite answer in terms of > natural numbers. Mathematically the number of EC states can be modelled > as _function_ of time. > > > The set of prime numbers does not contain the number 1. > > According to a widespread defintion of "prime number" the set of prime > numers _refers_ _to_ a set which does not contain the number 1. > > > But once upon a time it did contain it. > > There may have been a time, when _a_ _different_ _set_ (one containing > the 1) was _referred_ _to_ _by_ the named "set of prime numbers". That is a matter of definition. It was *the* set of prime numbers. But it is really superfluous to reply that, according to your definition, it was another set. Of course it was another set, because the set of prime numbers has changed. > > This does not imply that the set of former times "has changed" in time. > Only the naming has changed due to a changed definition. You may > compare this with Gerhard Schröder who did not undergo a gender > transformation when Angela Merkel became chancellor in 2005. > But "the chancellor" did. Regards, WM
From: Sebastian Holzmann on 6 Dec 2006 10:30
Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/5/2006 10:54 PM, Virgil wrote: >> 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) You don't. >> EB should read what axioms of extensionality actually says before >> pontificating. |