Cantor Confusion
in [Math]
|
From: mueckenh on 13 Feb 2007 05:31 On 12 Feb., 17:38, Franziska Neugebauer <Franziska- Neugeba...(a)neugeb.dnsalias.net> wrote: > mueck...(a)rz.fh-augsburg.de wrote: > > On 12 Feb., 13:59, Franziska Neugebauer <Franziska- > > Neugeba...(a)neugeb.dnsalias.net> wrote: > >> mueck...(a)rz.fh-augsburg.de wrote: > >> > Set theory, however, says: If the union of all finite paths, > >> > 0., 0.0, 0.00, 0.000, ... , > >> > is in the tree, then the infinite path p(oo) = 0.000.... is in the > >> > tree too. > > >> No contemporary set theory or graph theory does posit such a > >> nonsensical claim. It is entirely *your* claim, better known as > > > It is easy to recognize from the union of all finite segments of N. > > Set theory says: If the union of all finite segments, > > {1,2,3,...,n} is present, > > "Present"? Where? That question should be answered by those person who claim the existence. But to make it easy for you: It is claimed that N exists as the union of its initial segments. > > > then the infinite set N = {1,2,3,...} is present. > > Where? I don't know of any contemporary set theory which states that > entities are "present". It is stated that sth "exists". Can something exist without being present somewhere? > > Or do you see a difference betwee n the union of all finite segments > > and N? > > First of all I don't see that contemporary set or graph theories posit > > | Set theory, however, says: If the union of all finite paths, > | 0., 0.0, 0.00, 0.000, ... , > | is in the tree, then the infinite path p(oo) = 0.000.... is in the > | tree too. Then you deny that N is the union of all of its initial segments? Or do you deny that the nodes corresponding to the paths 0., 0.0, 0.00, 0.000, ... , can be mapped on the initial segments of N? Perhaps certain mappings are forbidden? Regards, WM
From: mueckenh on 13 Feb 2007 05:44 On 12 Feb., 18:08, Franziska Neugebauer <Franziska- Neugeba...(a)neugeb.dnsalias.net> wrote: > mueck...(a)rz.fh-augsburg.de wrote: > > On 12 Feb., 14:29, Franziska Neugebauer <Franziska- > > Neugeba...(a)neugeb.dnsalias.net> wrote: > > >> > The connectedness is given by the stucture of the tree. > > >> Your claim is: > > >> | >One cannot determine merely from a set of nodes for a given > >> | >tree whether that set of nodes is or is not a path. [<-- FN] > >> | One can. [<-- WM] > > >> As I have shown in my example one cannot. How long do you want to > >> argue against facts? > > > All you have shown is that some clumsy notation is always capable of > > destroying meaning. > > "For they sow the wind, and they will reap the whirlwind. He has no > standing grain. The stalk will yield no head. If it does yield, > strangers will swallow it up." Delicious! Dominus regnabit in aeternum et ultra. Amen. > >> > Given my fixed coordinate system, there remains no ambiguity at > >> > all. > > >> Then we are no longer talking about binary trees in general. > > > I never did so. > > I couldn't agree more. Why then did you claim the opposite? Did you lie? > > > (I like trees in nature, like the trees in the Harz mountains, but I > > have no special connection to trees of graph theory.) > > That confirms my assessment. > Then focus on the only important tree in this general proof, please. Regards, WM
From: mueckenh on 13 Feb 2007 05:49 On 12 Feb., 20:21, "MoeBlee" <jazzm...(a)hotmail.com> wrote: > On Feb 10, 5:38 am, mueck...(a)rz.fh-augsburg.de wrote: > > > On 9 Feb., 21:26, "MoeBlee" <jazzm...(a)hotmail.com> wrote: > > > > > Reality. > > > > What reality? Empirically testable physical reality? A mathematical > > > statement is not of that kind. > > > Every mathematical statement is of that kind. > > You snipped the rest of my argument regarding this. > > > You would recognize this > > (if you could, but you couldn't) if all reality ceased to exist. No > > mathematics would remain. Yes, to grasp these facts, without such a > > bad experience, i.e., during the continued existence of reality, one > > needs some deeper thinking than is required to understand the meaning > > of some crazy axioms. > > Yes, if nothing existed, then mathematics would not exist, whatever it > might be for there to be nothing that exists. Fortunately, we can do > mathematics without consternation over such mind-boggling > hypotheticals. You can do mathematics without seeing its foundation (which are not axioms or logic but reality) but you cannot do mathematics without using it. Do you think it is wise to do something without being able or willing to see its ground? Angels may be able to fly in the ether, mathematicians are not. Regards, WM
From: mueckenh on 13 Feb 2007 06:00 On 12 Feb., 21:02, Virgil <vir...(a)comcast.net> wrote: > In article <1171281091.730079.207...(a)a34g2000cwb.googlegroups.com>, > > mueck...(a)rz.fh-augsburg.de wrote: > > On 11 Feb., 18:32, "Mike Kelly" <mk4...(a)bris.ac.uk> wrote: > > > On 11 Feb, 14:58, mueck...(a)rz.fh-augsburg.de wrote: > > > > I say 111 is number 7. Now what? > > > The binary meaning is a convention and does not refute or change the > > unary meaning of 111. > > But it does show that /the/ meaning of "111" lies purely in the eye of > the beholder, and not in the expression itself. No. Beauty may. One hundred and eleven or 7 or any other meaning may also lie in the eye of the beholder. But the meaning of 3, i.e., *all* that 3 can express, lies objectively in 111. Regards, WM
From: mueckenh on 13 Feb 2007 06:07
On 12 Feb., 21:22, Virgil <vir...(a)comcast.net> wrote: > In article <1171283208.696664.25...(a)a75g2000cwd.googlegroups.com>, > > mueck...(a)rz.fh-augsburg.de wrote: > > On 12 Feb., 04:13, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > > In article <1171205918.124082.214...(a)a75g2000cwd.googlegroups.com> > > > mueck...(a)rz.fh-augsburg.de writes: > > > > > On 11 Feb., 03:06, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > > ... > > > Well, I would concede that the above three things are representaions of the > > > number three, using some convention. Anyhow, they are *not* the number > > > three. > > > What has "the number three" that is not expressed above? > > Universality. Just as no single man represents mankind, I did not say that III expresses all numbers. It expresses all that the number 3 can express. > no single > instance of a set with three objects represents all sets of three > objects, at least without common consent. What about all exsting sets with 3 objects, i.e., the fundamenal set of 3? Regards, WM |