Cantor Confusion
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From: mueckenh on 30 Jan 2007 08:47 Franziska Neugebauer schrieb: > mueckenh(a)rz.fh-augsburg.de wrote: > > > The proof has been given. > > In which peer-reviewed journal? Which proof are you talking about? Regards, WM
From: Fuckwit on 30 Jan 2007 09:47 On 30 Jan 2007 05:47:09 -0800, mueckenh(a)rz.fh-augsburg.de wrote: >>> >>> The proof has been given. [WM] >>> >> In which peer-reviewed journal? >> > Which proof are you talking about? > Huh? :-o The proof which has been given (as *you* just claimed)! Fuckwit Complete dialog: ------------------------------------------------------ FN: "In the framework of ZFC it _is_ fact that the set of all natural numbers does not have a maximum. Without a proof of a contradiction _within_ the ZFC framework there is no reason for your disfavour." WM: "The proof has been given." FN: "In which peer-reviewed journal?" WM: "Which proof are you talking about?" ------------------------------------------------------ *lol* Good one, WM!!! :-)
From: Dave Seaman on 30 Jan 2007 10:17 On Tue, 30 Jan 2007 13:45:59 GMT, Andy Smith wrote: > Just following up the idea of countability. > Am I right in thinking that any set of "finitely describable" objects is > necessarily countable? - on the grounds that "finitely describable" > implies that there exists some (multi-dimensional) address space which > uniquely defines an object, and that that address is indexable by a > finite set of natural numbers, and then that that multi-dimensional > address (as with the "standard arrangement" for counting the rationals) > can be ordered such that each address has a unique index in the natural > numbers? Yes. The number of "descriptions" is countable. > On that basis I would surmise that e.g. the set of all roots of all > polynomials with rational coefficients are countable - is that correct? Yes. What you have just stated is that the set of algebraic numbers is countable. We can make a slightly stronger statement: the set of computable numbers is also countable. That includes all of the algebraic numbers and also some transcendentals such as pi and e, plus all the numbers that can be derived from them. -- Dave Seaman U.S. Court of Appeals to review three issues concerning case of Mumia Abu-Jamal. <http://www.mumia2000.org/>
From: Franziska Neugebauer on 30 Jan 2007 11:18 mueckenh(a)rz.fh-augsburg.de wrote: > Franziska Neugebauer schrieb: >> mueckenh(a)rz.fh-augsburg.de wrote: [...] >> "You are in error. The union of the trees T(n) and T(n+1) is >> defined. n is a natural number. Therefore the union of all >> finite trees is defined." >> >> had been cut by your. > > Why should we repeat such self-evident truth again and again? LOL >> >> You may take >> >> notice of the similar claim: >> >> >> >> "The sum of the numbers n and n + 1. n is a natural number. >> >> Therefore the sum of all finite numbers is defined." >> > >> > If all natural numbers existed, why shouldn't their sum exist? >> >> 1. Your reasoning if flawed. The latter does not follow from the >> former. It is *not* "covered" by induction. > > You can try to utter again and agan this nonsense, I am uttering against that nonsense of yours. [...] >> >> 2. BECAUSE it is _undefined_ until the "sum of all natural numbers" >> is defined. > > It is defined if the set of all natural numbers s defined, Wrong and non sequitur. [...] F. N. -- xyz
From: Franziska Neugebauer on 30 Jan 2007 11:18
mueckenh(a)rz.fh-augsburg.de wrote: > Franziska Neugebauer schrieb: > Continued [nonsense] >> >> 2. BECAUSE it is _undefined_ until the "sum of all natural numbers" >> is defined. > > This sum is defined by > I > II > III > ... > > i.e. by this set of symbols "I", each of which is to be identified by > its index. I cannot see any sum here. F. N. -- xyz |