Cantor Confusion
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From: David Marcus on 2 Feb 2007 22:28 mueckenh(a)rz.fh-augsburg.de wrote: > Here is the definition of the set N > > 1 > 2 > 3 > ... > > Here is the definition of the sum of all elements of N > > 1 > 23 > 456 > ... That's pretty impressive. Did you come up with that all by yourself? -- David Marcus
From: Virgil on 2 Feb 2007 22:50 In article <eq0nil$ate$1(a)news2.open-news-network.org>, Carsten Schultz <carsten(a)codimi.de> wrote: > mueckenh(a)rz.fh-augsburg.de schrieb: > > 4 is the set of all sets with 4 elements. 4 is also every set with 4 > > elements. > > From that it follows that there are exactly four sets with four > elements, since these are the elements of 4. It also follows that there > is only one set with four elements, namely four. So 4=1. You should > write a book about this. He did! Just ask him!
From: David Marcus on 3 Feb 2007 11:38 mueckenh(a)rz.fh-augsburg.de wrote: > On 2 Feb., 02:42, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > In article <1170348637.768496.237...(a)a75g2000cwd.googlegroups.com> mueck...(a)rz.fh-augsburg.de writes: > If there is an infinite pathlength, then there must be an infinite > number It is hard to believe that anyone could actually believe this is correct. Quite remarkable. > > > > > > Wrong. Infinite paths do not have a path-length that is a > > > > > > natural number. > > > > > > > > > > Pathlengths ARE natural numbers. > > > > > > > > For finite paths. > > > > > > In all cases, by definition. > > > > *What* definition? > > Definition: Map the pathlength x on the number x. Hard to believe that anyone could consider this to be a definition. Quite remarkable. -- David Marcus
From: David Marcus on 3 Feb 2007 11:41 Virgil wrote: > In article <45c31c0b$0$97214$892e7fe2(a)authen.yellow.readfreenews.net>, > Franziska Neugebauer <Franziska-Neugebauer(a)neugeb.dnsalias.net> wrote: > > mueckenh(a)rz.fh-augsburg.de wrote: > > > On 2 Feb., 02:42, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > >> However, when we construct the path: > > >> p = {n_1} U {n_1, n_2} U {n_1, n_2, n_3}, ... > > >> we get as path: > > >> {n_1, n_2, n_3, n_4, ...} > > >> the path length in this case is *not* a natural number. It is the > > >> cardinality of N. > > > > > > The pathlength is not a natural number but it is a number (by > > > definition), namely omega. You see that there is no infinite set N > > > without an infinte number in it. > > > > As omega is not member of N I don't see that. > > Also, every natural is either even or odd but not both. > is omega even or odd? You are missing a WM axiom: Path lengths are natural numbers (even for infinite paths). -- David Marcus
From: Lester Zick on 3 Feb 2007 12:30
On Sat, 3 Feb 2007 11:38:54 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >mueckenh(a)rz.fh-augsburg.de wrote: >> On 2 Feb., 02:42, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: [. . .] >> > *What* definition? >> >> Definition: Map the pathlength x on the number x. > >Hard to believe that anyone could consider this to be a definition. >Quite remarkable. No more remarkable than what you consider to be a definition. ~v~~ |