Cantor Confusion
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From: mueckenh on 11 Jan 2007 11:49 Franziska Neugebauer schrieb: > >> 2. "Always finite" makes no sense or is contradictory. "Always" > >> refers to a temporal aspect which is not present in mathematics due > >> to the lack of time. Finite in size implies having a last element. > > > > This and your further questions are answerd by the following texts. > > I did not pose any questions. I have informed you about the fact that > there is no time and hence no temporal process _in_ math. Be informed then that mathematics is in time. Here you can find some more information: http://www.fh-augsburg.de/~mueckenh/MR/PUundAU.htm http://www.fh-augsburg.de/~mueckenh/MR/Publ.mht [Brouwer] maintains that a veritable continuum which is not denumerable can be obtained as a medium of free development; that is to say, besides the points which exist (are ready) on account of their definition by laws, such as e, pi, etc. other points of the continuum are not ready but develop as so-called choice sequences. [Fraenkel, Abraham A., Bar-Hillel, Yehoshua, Levy, Azriel: Foundations of Set Theory, North Holland, Amsterdam (1984) p. 255] Trotz wesentlicher Verschiedenheit der Begriffe des potentialen und aktualen Unendlichen, indem ersteres eine veränderliche endliche, über alle Grenzen hinaus wachsende Größe, letztere ein in sich festes, konstantes, jedoch jenseits aller endlichen Größen liegendes Quantum bedeutet, tritt doch leider nur zu oft der Fall ein, daß das eine mit dem andern verwechselt wird. [G. Cantor, Gesammelte Anhandlungen, p. 374] Regards, WM
From: Franziska Neugebauer on 11 Jan 2007 11:53 mueckenh(a)rz.fh-augsburg.de wrote: > Franziska Neugebauer schrieb: >> mueckenh(a)rz.fh-augsburg.de wrote: >> > Franziska Neugebauer schrieb: >> >> ,----[ <45a3ae6b$0$97254$892e7fe2(a)authen.yellow.readfreenews.net> ] >> | No. I do refer to "complete" in the sense of "finished" in contrast >> | to "potential" inifite. Since neither the list and hence nor the >> | diagonal is finite there are no largest elements. OTOH since we do >> | not assume every member of the list or the diagonal to provably >> | exist, the list and the diagonal are "potential" infinite. >> | >> | This said William Hughes has shown that the assumption of the >> | exist[e]nce of a "potentially infinite" "last line" L_D leads to a >> | contradiction. Hence "L_D exists" is wrong. >> `---- >> >> So you agree to this part you have cut? Fine! > > There exist only some members "since we do not assume every member of > the list or the diagonal to provably exist". Or what does it mean that > we do not assume every member to provably exist (actually)? Only every > second member exists (actually)? It simply means: We do not use the "every element exists" in the proof. >> >> Since there is no largest element in "potentially" infinite sets >> >> (in "actual/complete/finished", too) this sentence makes no sence >> >> at all. >> > >> > A potentially infinite quantity (set or not) is always finite. >> >> There is no time in maths. > > But maths is in time. Dyslexia again? > God, if existing, may be out of time. But even worshipping sets does > not make them divine. > >> >> > If it turns out, that the diaogonal has a larger element, then >> >> > it turns out that a line containing this (and all smaller ones) >> >> > does also exist. >> >> >> >> > In any case, a line containig all elements of the diagonal does >> >> > exist. >> >> >> >> Proof? > > It is the set of all existing numbers. > >> > The existence of the diagonal (if existing) and the fact that a >> > given set of natural numbers is always a subset of a natural >> > number. >> >> Why not say "the pope said so"? > > Because I can show of every set of natural numbers *given to me* that > it belongs to one line (= finite set). That is rather unintersting. F. N. -- xyz
From: mueckenh on 11 Jan 2007 11:55 Franziska Neugebauer schrieb: > mueckenh(a)rz.fh-augsburg.de wrote: > > > Franziska Neugebauer schrieb: > >> >> > A potentially infinite quantity (set or not) is always finite. > >> >> > >> >> There is no time in maths. > >> > > >> > So you write these letters and develop new ideas in zero time? > >> > >> My posts and my ideas do not take place *in* maths. They take place > >> in the real _physical_ world. > > > > So does the contents of your posts and ideas, in part mathematics. > > This does not invalidate the fact that in mathematics there is no notion > of time. A disadvantage or error which need not perpetuate in eternity (et ultra). >And hence in mathematics there are no temporal processes. This > said "always" is not a intra-mathematically defined notion. There are mathematicians greater than you and any living set terrorists which are convinced of the opposite. > > From this follows: "A potentially infinite quantity (set or not) is > always finite" is a meaningless sentence. Everything you don't understand seems meaningless to you. > > >> > There is no existence outside of time. > >> > >> _Mathematical_ existence is not to be confused with physical > >> existence. A mathematical entity x exists if there is a proof of "x > >> exists". > > > > There is no proof existing outside space and time. > > This is an argument supporting which claim? Time is important in mahematics. > > >> As I have pointed out many times before: If and if so how the > >> physical world determines our reasoning is off topic in sci.math. > >> Please consult the neuro sciences groups for that complex of issues. > >> > >> This said your statement "A potentially infinite quantity (set or > >> not) is always finite" makes no sense. > > > > Read the texts by Cantor and Hilbert given in my recent contribution. > > I don't understand the fragments you have posted. Read the full texts. I gave the sources. > They represent > obviously merely a philophical discussion which do cannot understand. > > Perhaps you better reword the texts in your own lingo. If you want to > state a different opinion to Cantor/Hilbert you should do so, too. > > Hence your sentence "A potentially infinite quantity (set or not) is > always finite" still makes no sense. If it makes any sense you could > explain that sense in your own words. Explain colour to a blind? Regards, WM
From: Franziska Neugebauer on 11 Jan 2007 11:57 mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > >> > > > No. But the property of being the greatest line can and does >> > > > change. >> > > >> > > Irrelevant. The question is whether L_D exists. >> > >> > It does. Does the tallest man exist? When did it start, when did it >> > cease? >> >> Recall: >> >> L_D is a line that contains every element that can >> be shown to be in the diagonal. >> >> >> The "tallest man" is something that can change. L_D is a line. >> A line cannot change. The analogy is not valid. > > L_D is the name of a line, like a championship title. Which you definitely never won neither in maths nor in logic. >> > > It is possible to find L_D >> > >> > It is not assumed, but it is obvious that for every given set of >> > natural numbers there is one line containing it. >> >> But since the set of natural numbers can change >> this "one line" can change. It is not L_D. >> >> > > >> > > If you assume actual infinity then L_D >> > > does not exist. >> > >> > It does exist, in potential infinity. But it is not fixed. >> >> L_D is a line. A line is fixed. L_D does not >> exist. > > It is the line containing the whole set. The existence of which has already been refuted successfully. >> > > Therefore you cannot assume actual infinity. >> > > >> > > You now admit that it is not possible to find L_D, >> > >> > In actual infinity (everything including L_D being fixed) it is not >> > possile to find L_D. >> >> And it is also not possible to find L_D in potential infinity. > > Let L_D go from 1 to oo. We let L_D go. F. N. -- xyz
From: Franziska Neugebauer on 11 Jan 2007 12:10
mueckenh(a)rz.fh-augsburg.de wrote: overdue: ,----[ <45a62aa2$0$97272$892e7fe2(a)authen.yellow.readfreenews.net> ] | > He misundertands the meaning of potential infinity. | | 1. Please explain what exactly he misunderstands. | | 2. Does he use a wrong definition of "potentially infinite set"? | If so, please give the "right" one, you want to base your game on. `---- > Franziska Neugebauer schrieb: > > >> >> 2. "Always finite" makes no sense or is contradictory. "Always" >> >> refers to a temporal aspect which is not present in mathematics >> >> due to the lack of time. Finite in size implies having a last >> >> element. >> > >> > This and your further questions are answerd by the following texts. >> >> I did not pose any questions. I have informed you about the fact that >> there is no time and hence no temporal process _in_ math. > > Be informed then that mathematics is in time. From that it does not follow that there is a notion of time in mathematics. Hence your objection is irrelevant. There is no time in maths and hence there are no temporal processes in math. At least everywhere but in Augsburg. > Here you can find some more information: > http://www.fh-augsburg.de/~mueckenh/MR/PUundAU.htm > http://www.fh-augsburg.de/~mueckenh/MR/Publ.mht My provider has closed off your server due to obnoxious content. > [Brouwer] maintains [...] Please tell us, whether you want to discuss views of [ ] Cantor [ ] Brouwer [ ] Mueckenheim [ ] Cantor interpreted by Mueckenheim [ ] Brouwer interpreted by Mueckenheim. If more than one applies please tag each sentence of yours accordingly. You'd better rephrase it in English anyhow. F. N. -- xyz |