Cantor Confusion
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From: Eckard Blumschein on 5 Dec 2006 13:05 On 12/5/2006 2:22 PM, mueckenh(a)rz.fh-augsburg.de wrote: > Eckard Blumschein schrieb: > >> On 12/1/2006 3:10 PM, mueckenh(a)rz.fh-augsburg.de wrote: >> > Eckard Blumschein schrieb: >> > >> > >> >> I recall being a little boy wondering when I was told that while there >> >> is no evidence proving the existence of god there is also no evidence >> >> showing his non-existence. Are those crippled who don't believer in CH? >> >> I consider the background of CH given in the difference between number >> >> and continuum. This might be crippled down to the truth? Do you agree? >> >> >> > No, I am sorry, I do not. The continuum is nothing but our failure to >> > look closely enough. In physics it lasted 2000 years to settle the idea >> > of the atom and to supplement and complete it by the uncertainty >> > relations. The majority of matematicians is not yet far sighted enough >> > to recognize the same situation in their realm. > >> Why should we abandon the old and proven concepts number and continuum? >> To my understanding, they may or may not ideally fit the reality. Even >> after I know that solids consist of molecules, atoms, and smaller >> particles, there is no reason to start at this insight when designing >> let's say a building. > > There is no reason to give up continuity for applied mathematics. Ony > those who want to learn the real truth may bother. Not even those. > > Regards, WM >
From: Eckard Blumschein on 5 Dec 2006 13:13 On 12/5/2006 2:45 PM, Dik T. Winter wrote: > > I wonder why the mathematicians believe to require one-point > > compactification. I consider the rationals as genuine numbers, being as > > close as you like to the fictions infinity and real numbers. The exact > > numerical representation of pi requires the fiction of actual infinity. > > I wonder why you are talking about things you know nothing about? Who > requires one-point compactification with what goal? When I presented ideas in connection with http://iesk.et.uni-magdeburg.de/~blumsche/M283.html I faced scepticism or refusal as well as the hint to compactification. I consider my ideas still flawless. I even found plausible answers to several questions no mathematician was able to provide a convincing answer to. So I doubt about fundamentals which require compactification.
From: Eckard Blumschein on 5 Dec 2006 13:15 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?
From: Eckard Blumschein on 5 Dec 2006 13:26 On 12/5/2006 4:10 PM, Bob Kolker wrote: Futilities > Eckard Blumschein wrote: > >> sinde and generally uncountable just fictitious reals on the other side. >> >> In other words: Genuine numbers are countable, fictitious numbers are >> uncountable. The latter do not have an available numerical address. > > For the latest time: countability is a property of sets, not individual > numbers. Sets are uncountable because they do not consist of discrete numbers. They are countable it they consist of discrete numbers. If you like perform a bijection between them. > > There is no such thing as a countable integer, countable rational or > countable real. Reals according to DA2 are fictitious and therefore not addressable und eventually uncountable. Any single integer can be an element of something countable. > Bob Kolker >
From: MoeBlee on 5 Dec 2006 14:10
Bob Kolker wrote: > There is no such thing as a countable integer, countable rational or > countable real. In the sense you're trying to get across to the other poster, I understand your point. But, just for the record, in a technical sense in set theory, as integers, rational numbers, and real numbers are themselves sets, it does make sense to say whether one of them is countable or not. For example, where integers are defined as equivalence classes of natural numbers, each integer is itself a denumerable set. I am not necessarily endorsing anything the other poster has said; I'm just adding the technical note that in a strict set theoretic sense, even numbers are sets and thus it is meaningful to talk about the cardinality of a number. MoeBlee |