Another AC anomaly?
in [Logic]
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From: WM on 27 Dec 2009 13:01 On 22 Dez., 15:47, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > In article <b484e377-9dc2-424b-80c3-2912165f6...(a)a32g2000yqm.googlegroups..com> WM <mueck...(a)rz.fh-augsburg.de> writes: > > On 21 Dez., 14:23, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > ... > > > > That you cannot get step by step to 1/0 does not mean that it does not > > > > exist? > > > > > > Indeed. On the projective line (that precedes Cantor by quite some time > > > as far as I know) it does exist. > > > > But does the projective line exist? > > Exist in what sense? But it is a concept from projective geometry, but > perhaps you think that is also nonsense? I may note that the point at > infinity was developed by Kepler and Desargues in the 17th century. Nevertheless it has been used already by Pietro Perugino in a Fresco at the Sistine Chapel, in 1482. > > > > I studied mathematics and a university council > > appointed me to teach mathematical lessons. > > Well, the same did hold for my father, He taught math over 20 years at universities and wrote a book or two on math? > but he never considered himself > a mathematician, but a physicist. > You may note that I deny to be a matheologian, i.e. a member or element of the set of those who consider infinity to be finished and uncomputable numbers being computable, i.e., being numbers. Regards, WM
From: Marshall on 27 Dec 2009 13:15 On Dec 27, 9:57 am, WM <mueck...(a)rz.fh-augsburg.de> wrote: > On 22 Dez., 15:28, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > > > Even a matheologian should understand that: If there is no digit at a > > > finite place up to that the sequence 0.333... identifies the number > > > 1/3, then there is no digit at a finite place up to that the number > > > 1/3 can be identified. > > > Right, there is no digit at a finite place up to that the number 1/3 can be > > identified. And as there are no digits at infinite places that appears to > > you to be a paradox. It is not. There is *no* finite sequence of digits > > that identifies 1/3. But there is an *infinite* sequence of digits that > > does so. > > Why not pronounce it a bit clearer? We know that every digit is the > last digit of a finite initial segment of digits. There is no other > digit, is it? > Therefore your statement can be expressed in the following way: There > is no finite initial segment that identifies 1/3. But there is an > infinite finite initial segment that identifies 1/3. So you consider "infinite finite initial segment" as a clearer but equivalent form of "infinite sequence of digits". I guess you don't know what a sequence is. Or what infinite means. I'm going to give you the benefit of the doubt on "digits." > If you read this sentence, perhaps you get an impression of what > matheology is? Yes! It is your projection of your own inability to think clearly onto others. > > > I said, if there is a sequence that identifies > > > 1/3, then the identifying digits must be at finite places. > > > Right, all identifying digits (there are infinitely many) are at finite > > places. > > Therefore your statement can be expressed in the following way: There > is no finite initial segment that identifies 1/3. But there is an > infinite finite initial segment that identifies 1/3. Every time you use the phrase "infinite finite" you look stupid. If only you were as dumb as you are stupid! > > > Does the sequence of 1/3 not consist of a union of all finite > > > initial segments? > > > It is, but also (according to *your* definition) it is not a path. > > There can be no question: The union of all finite initial segments is > finite. You have found another way to say "infinite finite" and hence another way to look stupid. Marshall
From: Ross A. Finlayson on 27 Dec 2009 15:23 On Dec 22, 5:38 pm, Marshall <marshall.spi...(a)gmail.com> wrote: > On Dec 22, 5:27 pm, "Ross A. Finlayson" <ross.finlay...(a)gmail.com> > wrote: > > > On Dec 19, 5:20 pm, Virgil <Vir...(a)home.esc> wrote: > > > > Not at all! > > > > I merely note that every rational integer is included among the reals, > > > in both the Dedekind construction and the Cauchy construction, and 1 is > > > nicely both rational and integral. > > > Oh, so 1 = 1.000... now, eh. > > > Good luck with that. > > He won't need it. 1 the ratio is the same number as 1 > the natural, is the same number as 1 the member of > any other set. > > Unless you confuse numbers and their representations. > > Marshall In set theory there are only sets. Of course I think that 1 = 1.000..., but it makes a Platonist out of you. Consider the general construction via ordinals of the naturals, vis-a- vis a standard construction of the reals. If you want to encode their representations then it's of products of sets, for example those. So, implicitly, writing "1 = 1.000..." encodes both of them. There are simpler ways to model various real-valued processes. There are more obvious consequences, more of them. Area is the sum. Rationals have much simpler encodings than the general standard case, which finds itself "incomplete" in being the "complete" ordered field, in that each arithmetic operation would be definite, constructively then via completeness, Dedekind/Cauchy/Eudoxus constructions are insufficient to model the real, real numbers, number-theoretically. Rationals are dense in the reals. Ross
From: Ralf Bader on 27 Dec 2009 15:42 WM wrote: > Why not pronounce it a bit clearer? We know that every digit is the > last digit of a finite initial segment of digits. There is no other > digit, is it? > Therefore your statement can be expressed in the following way: There > is no finite initial segment that identifies 1/3. But there is an > infinite finite initial segment that identifies 1/3. > > If you read this sentence, perhaps you get an impression of what > matheology is? If one reads your statements over the years one gets an impression what stupidity is.
From: Virgil on 27 Dec 2009 15:49
In article <c003a30a-d96a-4d67-a879-dd22db35c721(a)g26g2000yqe.googlegroups.com>, WM <mueckenh(a)rz.fh-augsburg.de> wrote: > On 22 Dez., 15:47, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > In article > > <b484e377-9dc2-424b-80c3-2912165f6...(a)a32g2000yqm.googlegroups.com> WM > > <mueck...(a)rz.fh-augsburg.de> writes: > > �> On 21 Dez., 14:23, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > ... > > �> > �> That you cannot get step by step to 1/0 does not mean that it does > > not > > �> > �> exist? > > �> > > > �> > Indeed. �On the projective line (that precedes Cantor by quite some > > time > > �> > as far as I know) it does exist. > > �> > > �> But does the projective line exist? > > > > Exist in what sense? �But it is a concept from projective geometry, but > > perhaps you think that is also nonsense? �I may note that the point at > > infinity was developed by Kepler and Desargues in the 17th century. > > Nevertheless it has been used already by Pietro Perugino in a Fresco > at the Sistine Chapel, in 1482. Which in no way refutes the work of Kepler and Desargues. > > > > > > > �> � � � � � � � � �I studied mathematics and a university council > > �> appointed me to teach mathematical lessons. > > > > Well, the same did hold for my father, > > He taught math over 20 years at universities and wrote a book or two > on math? > > > but he never considered himself > > a mathematician, but a physicist. > > > > You may note that I deny to be a matheologian Since your "matheologia" is a creature of your own invention and exists nowhere except in your own mind, you are its father and mother and only possible child. |