Cantor Confusion
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From: Bob Kolker on 6 Dec 2006 10:35 Eckard Blumschein wrote: > > > They are categorically quite different. According to Peirce, fictitious > numbers are mere potentialities. According to Brouwer and Pratt they do > not obey trichotomy. > Who denies their quite different properties will never understand what > makes the rationals different from the reals. The thread nightmare real > numbers has been lasting since September the 9th until now. > I admit, mathematicians are not trained to grasp the difference between > quantity and quality. And the use of these fictions has lead to solutions of mathematical problems which have produced useful applications. Without these fictions there would not be sufficient physics to produce the computers on which you type your blather. The results validate the methodology. Intuitionists like Brower and Heyting have produced few basic results in theoretical mathematics than have the mathematicians who are not as "fastidious". Consider, for a moment, the delta function. Taken literally, it is nonsense, yet it can be justified mathematically and has been indespensible for the formulation of quantum field theory. Bob Kolker
From: Bob Kolker on 6 Dec 2006 10:37 Eckard Blumschein wrote: > > Dedekind as well as Cantor started from this idea. Cantor even > fabricated the notion cardinality in order to quantify the putative Formulated, not fabricated. Strictly speaking ALL mathematics is fabricated. Every last bit of it. Even the arithmetic of integers is fabricated since it is based on the fiction of the integer 1 and the successor function as well as the indiction principle. Bob Kolker
From: Bob Kolker on 6 Dec 2006 10:38 Eckard Blumschein wrote: > > 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. What is "potential" infinity. Can you define it rigorously? Bob Kolker
From: Bob Kolker on 6 Dec 2006 10:39 Eckard Blumschein wrote: > Set theorist may wish this. No my arguments are real and unrefuted. > There is not just the so called 4th possibility. I indeed applies. Your arguments are nonsense. Unsinn! They have no mathematicial validity whatsoever. Bob Kolker
From: mueckenh on 6 Dec 2006 10:39
Franziska Neugebauer schrieb: > mueckenh(a)rz.fh-augsburg.de wrote: > > > Bob Kolker schrieb: > [...] > >> Rational numbers are non-genuine. Nowhere in the physical world > >> outside of our nervouse systems do they exist. > > > > The nervous system is a part of the physical world. > > Hence this issue is to be disussed in a physics or neuro sciences > newsgroup. > > > The integers belong to the nervous system. > > The nervous system is generally not an issue in mathematics. That is why many mathematicians overestimate their capabilities so grossly. > > > They would not exist without the nervous system. > > This is a miscomprehension. Mathematical numbers exist mathematically. And nobody knows what has to be understood by this sentence. > If you want to discuss how abstract entities, i. e. naive numbers, > "exist" in the sense of "are represented in the neural system" > you should discuss this issue in an appropriate neuro sciences > newsgroup. New facts about the foundations of mathematics should be appropriate in a math news group. > > But some people nevertheless believe in the immortal soul. > > This is not a mathematical issue. It is a parallel. The belief in the inexistent: Soul - infinty. > > I think that is just as strange as the belief in one's > > own capability of imaging actual infinity. > > And, remarkably, the creator of this theory believed in both, the > > soul/God and actual infinity, > > It is remarkable that the former Generalfeldmarschall of Nazi Germany > Hermann Göring frequently spent his vacation in the Harz. Just like you > (and possibly Cantor, too,) do. To me it is not clear whether you > prefer to wander the trails of Cantor or that of Göring. What has that to do with mathematics? > > > trying to prove the latter by the existence of the former. > > Since mathematically there is not a "god" this "proof" was hardly a > mathematical one. It was. Believing in axioms and believing in God is closely connected. Regards, WM |