Cantor Confusion
in [Math]
|
Prev: Pi berechnen: Ramanujan oder BBP
Next: Group Theory
From: mueckenh on 8 Feb 2007 03:39 On 7 Feb., 16:59, Franziska Neugebauer <Franziska- Neugeba...(a)neugeb.dnsalias.net> wrote: > mueck...(a)rz.fh-augsburg.de wrote: > > On 6 Feb., 23:07, Virgil <vir...(a)comcast.net> wrote: > > >> > The basic way to establish IV c V is to use the numbers in their > >> > basic > >> > form IIII c IIIII. (Numbers *are* their representations.) > > >> Numerals are no more numbers than names are people. > > > Wrong! People can exist and do exist without names. Numbers cannot. > > Who has told you that? Whatever, Mückenheim axiom 2: > > "Numbers cannot exist without name" If you take all names (in the widest sense, including symbols and notations and defining equations) from a number and attach it to another number, what remains with the first? > > Let's call that numbers "named numbers". If the length of names "must" > be finite one can easily prove, that any set of named numbers has > cardinality <= card(omega). Of course. That is not new to me. Regards, WM
From: mueckenh on 8 Feb 2007 03:46 On 7 Feb., 19:31, Virgil <vir...(a)comcast.net> wrote: > > > > Present mathematics has nothing in common with existence. > > > > In present mathematics "existence" does not mean *physical* existence. > > > In present mathematics "existence" is meaningless. > > In present mathematics WM is meaningless. Maybe. But I would exist without these initials as well. > > > > > > [...] > > > > >> Existence is a mathematical thing when you can establish it by axioms > > > >> or through theorems based on axioms. Anything else is merely > > > >> phylosophy. > > > > > There is something called reality and another thing called matheology. > > > > The latter is taught in Augsburg. > > > No. That is a wrong statement. > > Certainly if what WM "teaches" corresponds to what WM claims here, WM > does not teach anything that can be seriously called mathematics If you consider a tree with fixed nodes and edges but differing sets of paths as serious mathematics, then you are right. And I am proud not to teach teach this. I would consider this idea of yours as a serious sign of fanatism or senile stubbornness. Regards, WM
From: mueckenh on 8 Feb 2007 03:50 On 7 Feb., 19:42, Virgil <vir...(a)comcast.net> wrote: > In article <1170851785.038841.94...(a)h3g2000cwc.googlegroups.com>, > > The potentially infinite set of even numbers is *constructed* by its > > segments > > > {2,4,6,...,2n} > > Except that what is merely potential cannot be a set, at least according > to any serious notion of how a set must behave. For something to be a > set in any standard set theory, its membership must be totally > determinate, not vague and ambiguous But the paths in the tree may remain vague and ambiguous? Don't they belong to set theoy? > > But there are no other than finite natural numbers. > > But more than finitely many of them. A fact which WM keeps overlooking. because it is completely irreleant in this framework. > > > > > This simple truth > > Which is not a simple truth at all but a nonsense expression. > AS for WM, mathematically speaking, the truth is not in him.- Zitierten Text ausblenden - It is in you. I know. You consist of truth. Regards, WM
From: mueckenh on 8 Feb 2007 03:55 On 7 Feb., 20:09, Virgil <vir...(a)comcast.net> wrote: > > > > But if you > > > > assume its existence, then you see that the reals are countable or > > > > that identical nodes yield different path systems, an idea which > > > > presumably only you can utter. > > > > I do not assume it, I prove it, > > > It is nonsense and remains nonsense to assume that a given tree has > > different path systems according to... according to what? > > That WM assumes nonsense does not obligate sensible people to accept it. "according to what?" was the question. > > > According to > > your emotional condition? > > My "emotional" condition at least allows me to take logic into account, > which WM's emotional condition does not. What logic governs the sets of different paths you proved in the tree? > Regards, WM
From: mueckenh on 8 Feb 2007 04:02
On 7 Feb., 20:12, Virgil <vir...(a)comcast.net> wrote: > In article <1170852299.543791.43...(a)m58g2000cwm.googlegroups.com>, > > mueck...(a)rz.fh-augsburg.de wrote: > > On 6 Feb., 20:48, Virgil <vir...(a)comcast.net> wrote: > > > In article <1170754974.135681.22...(a)p10g2000cwp.googlegroups.com>, > > > > > > > The simplest reason is that omega - n = omega for all n in N. > > > > > > Where did you get that from? Reference? EB? > > > > > You could even figure it out by yourself. > > > > If one needs to adopt WM's crazy assumptions in order to come to WM's > > > crazy conclusions, we are all better off without them. Both his > > > assumptions and his conclusions > > > Excuse me, these were Cantor's assumptions and conclusions. > > Not the crazy ones I am referring to. We talked about: omega - n = omega for all n in N. > > For instance, one of WM's crazy assumptions is that a set of naturals > which is not finite must contain a natural which is not finite. and cannot contain it! > > Does WM claim that Cantor ever assumed or concluded that? He created this theroy. He was not and could not be aware of all of its problems and implications. He needed 12 years to distinguis between ordinal and cardinal number. He needed over 20 years to exclude the set of all sets. (Further there is a well-known mental reason: He did not look for contradictions very hard, because it would have spoilt his pet.) Regards, WM |