Cantor Confusion
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From: Virgil on 24 Nov 2006 15:17 In article <45672F32.7090202(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 11/23/2006 10:43 PM, Virgil wrote: > > >> The ambiguity resides within the three points "..." > >> They may denote either actual or potential infinity. > >> > >> > >> >> Meanwhile I see mounting evidence for my suspicion that set theory is > >> >> some sort of (self?)-deception. > >> > > >> > EB sees what he tells himself he should see, regardless of whether there > >> > is anything there to see of not. > >> > >> Those who follow the discussion will not immediately change their > >> opinion but should have a chance for doing so. > > > > If one has a choice between a red hat and a green hat, merely saying > > "hat" does not avoid ambiguity, but prefixing "hat" with "red" or > > "green" does. > > > > Thus "sequence {1,2,3...}" or "set [1,2,3...}" are no more ambiguous > > that "red hat" or "green hat". > > As ambiguous as "hat" in the sense of as many red as you like and "hat" > in the sense the quality green includes something irrational: all of > indefinitely much. It would appear that EB cannot distinguish between red hats and green ones. Not only innumerate but colorblind.
From: Virgil on 24 Nov 2006 15:29 In article <4567329A.5040400(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 11/23/2006 10:40 PM, Virgil wrote: > > In article <45659C9B.8000800(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > >> How do you imagine bijection with a actually infinite set? > >> Notice: Actual infinity is a "Gedankending" something fictitious. > > > > > > Al numbers are "Gedankendingens" (if the is the right plural). > > The correct plural would be Gedankendinge. Thanks. > Fraenkel (p. 6) referiert Cantor: das als reines Gedankending offenbar > nichts widerspruchsvolles in sich birgt. > > Indeed, the actually infinite set is selfcontradictory. Then all numbers are self contradictory. > > > > >> I do not say it is unconceivable or nonsense. It is just unapproachable. > > > > I t is conceivable as it has been conceived. > >> > >> Moreover, potentially and actually infinite are mutually excluding points > >> of view. > > > > So one can round file one of them. Mathematicians, by and large, round > > file the first, anti-mathematicians sometimes round file both. > > I do not understand your idioms "round file" and "by and large". Next to my desk I have a round container in which I file things that I do not intend to keep. When it gets full, I transfer its contents to the trash. For "by and large" see http://www.google.com/search?hl=en&lr=&as_qdr=all&defl=en&q=define:By+and +Large&sa=X&oi=glossary_definition&ct=title > > Notice. Mathematics has to do with potential infinity when dealing with > genuine numbers. But strictly speaking it deals with the actual infinity > when considering real numbers and the continuum. Notice: All numbers are equally fictitious. None of them are any more genuine than others. They all exist only in the mind.
From: Eckard Blumschein on 24 Nov 2006 16:38 On 11/24/2006 9:15 PM, Virgil wrote: >> Not unexplained but best imagined via the application on time or space. > > Certainly unexplained by EB. > And one can easily imagine it as, say, as the succession of points > (n-1)/n in the rational open interval (0,1) which is "completed" in the > rational interval [0,1]. Just replacing ) by ] seems to be quite easy and natural. In my understanding, with really real numbers there is no difference between ] and ] at all.
From: Eckard Blumschein on 24 Nov 2006 16:39 On 11/24/2006 9:17 PM, Virgil wrote: >> As ambiguous as "hat" in the sense of as many red as you like and "hat" >> in the sense the quality green includes something irrational: all of >> indefinitely much. > > It would appear that EB cannot distinguish between red hats and green > ones. Not only innumerate but colorblind. Not enough phantasy?
From: Virgil on 24 Nov 2006 17:22
In article <4567663F.7040903(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 11/24/2006 9:15 PM, Virgil wrote: > > >> Not unexplained but best imagined via the application on time or space. > > > > Certainly unexplained by EB. > > And one can easily imagine it as, say, as the succession of points > > (n-1)/n in the rational open interval (0,1) which is "completed" in the > > rational interval [0,1]. > > Just replacing ) by ] seems to be quite easy and natural. > In my understanding, with really real numbers there is no difference > between ] and ] at all. No one is claiming a difference between ] and ]. But in , say, Dedekind cuts, there is a distinguishable difference between (0,1) and [0,1], based on whether those sets contain or do not contain their LUBs and GLBs as members. |