Galileo's Paradox
in [Math]
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From: Eckard Blumschein on 6 Dec 2006 10:33 On 12/5/2006 11:12 PM, Virgil wrote: > In article <4575825A.4020304(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> On 12/5/2006 12:18 AM, Virgil wrote: (deleted) >> > In article <45747E16.6020904(a)et.uni-magdeburg.de>, >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote:(deleted) >> >> > Eckard Blumschein wrote:(deleted) > > Turnabout! Surrender? You were welcome.
From: Eckard Blumschein on 6 Dec 2006 10:38 On 12/5/2006 11:14 PM, Virgil wrote: > In article <457584A4.3000108(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 12/5/2006 12:16 AM, Virgil wrote: >> > In article <4574755B.4070507(a)et.uni-magdeburg.de>, >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> >> 2*oo is not larger than oo. Infinity is not a quantum but a quality. >> > >> > Which "infinity" is that? >> >> We do not need different infinities. > > Cantor did. And showed why with two separate proofs. I pointed to the 4th and only correct possibility of interpretation to DA2. Do not hope for maintaining the proof concerning the power set. The reason why the power set is also uncountable is quite simpel: One needs perfectly _all_ natural numbers before the power set of IN can be calculated: 2^oo = oo. So the second proof is also pointless. Do you have a third one?
From: Bob Kolker on 6 Dec 2006 10:44 Mike Kelly wrote: > > > The set of finite binary strings is a subset of the set of finite > decimal strings. > > Then b) precludes them being the same size. > > They are also both the same size as the set of natural numbers. > > Thus they are the same size as each other. > > Contradiction. What contradiction? Item b above is simly a mapping of the binary sequences (not beginning with 0) to a subset of the integers. Where is the problem? Bob Kolker >
From: Eckard Blumschein on 6 Dec 2006 10:47 On 12/5/2006 11:21 PM, Virgil wrote: > In article <457586BB.9020406(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 12/5/2006 12:09 AM, Virgil wrote: >> > In article <45745B16.40202(a)et.uni-magdeburg.de>, >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> > >> >> On 12/1/2006 9:59 PM, Virgil wrote: >> >> >> >> > Depends on one's standard of "size". >> >> > >> >> > Two solids of the same surface area can have differing volumes because >> >> > different qualities of the sets of points that form them are being >> >> > measured. >> >> >> >> Both surface and volume are considered like continua in physics as long >> >> as the physical atoms do not matter. >> >> Sets of points (i.e. mathematical atoms) are arbitrarily attributed. >> >> There is no universal rule for how fine-grained the mesh has to be. >> >> Therefore one cannot ascribe more or less points to these quantities. >> >> >> >> Look at the subject: Galileo's paradox: The relations smaller, equally >> >> large, and larger are pointless in case of infinite quantities. >> > >> > Then length and area and volume comparisons of size must be fictional >> > measurements. >> >> I do not think so. You deliberately mistook the sentence. No measured >> length, area, or volume is infinite. > > But they are measures of fictional qualities in EB's rubric, so must be > uncountable. Get serious! >> >> >> >> > Sets can have the same cardinality but different 'subsettedness' because >> >> > different qualities are being measured. >> >> >> >> I do not know a German equivalent to subsettedness. >> > >> > It is the quality of being a subset. It is one, but not the only, >> > measure of set "size". >> >> Cantor claimed to have discovered different sizes of infinite sets. Who >> introduced subsettedness, and is it also quantified? > > The subset relation, as a partial ordering of sets, has been around as > long as sets. Well, I read the word subset (Teilmenge) but you are the first one who offers subsettedness. >> >> Standard mathematics may lack solid fundamentals. At least it is >> >> understandable to me. However, I admit being not in position to likewise >> >> easily understand what you mean with well-ordered subsettedness. >> > >> > The subset relation does not provide a well ordering of arbtrary sets. >> >> Nobody does provide a well-ordering of the irrationals. > > What has that to do with whether one can well order a set of sets by > inclusion? > > EB seems compelled to go off on tangents. I will perhaps never understand what you mean with well-ordered subsettedness. When I wrote well-ordering of the irreals, I expressed smiling.
From: Eckard Blumschein on 6 Dec 2006 10:51
On 12/5/2006 11:27 PM, Virgil wrote: > In article <1165333562.354313.109050(a)j44g2000cwa.googlegroups.com>, > "Tonico" <Tonicopm(a)yahoo.com> wrote: > >> Eckard Blumschein ha escrito: >> >> > On 12/4/2006 11:52 PM, Virgil wrote: >> > >> > >> I am an electrical engineer >> > > >> > > Shocking! >> > >> > Why? We love mathematics. >> *************************************************** >> Oh, I bet elec. eng. love maths; the problem seems to be that maths >> does not correspond AT ALL that love, at least in the case of several >> engineers...**sigh**...tough. >> Tonio > > Electrical stuff can be shocking to those who use it carelessly or abuse > it, Do you refer to the electric chair? and judging by EB's careless abuse of mathematics, he is at risk. |