Cantor Confusion
in [Math]
|
Prev: Pi berechnen: Ramanujan oder BBP
Next: Group Theory
From: Lester Zick on 11 Nov 2006 15:02 On Sat, 11 Nov 2006 12:50:10 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >imaginatorium(a)despammed.com wrote: >> David Marcus wrote: >> > Franziska Neugebauer wrote: >> > > David Marcus wrote: >> > > >> > > > [...] you are working with an infinite triangle [...] >> > > >> > > ,----[ http://en.wikipedia.org/wiki/Triangle ] >> > > | A triangle is one of the basic shapes of geometry: a polygon with >> > > | three vertices [...] >> > > `---- >> > > >> > > Are there really three vertices in WM's "triangle"? >> > >> > No. But, I don't think an "infinite triangle" needs to be a triangle. >> > However, I'm open to suggestions for what to call it. >> >> You could call it a "two-sided triangle". This might turn out to be >> useful in a quiz some day. > >I like that! Next Brian might get to work on a transfinite Zen Abacus. ~v~~
From: Lester Zick on 11 Nov 2006 15:04 On Fri, 10 Nov 2006 17:33:16 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >mueckenh(a)rz.fh-augsburg.de wrote: >> David Marcus schrieb: >> > > >> > > Exactly this is done by Cantor's definition given above: "It is allowed >> > > to understand the new number omega as limit to which the (natural) >> > > numbers n grow". This is a definition, at least for those >> > > mathematicians who know what "limit, number, grow" means. >> > >> > I seriously doubt that Cantor considered it to be a definition. If he >> > did, he wouldn't have said, "It is allowed to understand". Regardless, >> > it is not a definition by modern standards. >> >> Who judges what modern standards are, in your opinion? > >A silly question. You haven't even bothered to learn the current meaning >of the word "definition". If you would actually read a textbook or take >a math course at a university, you might learn something. Curious coming from one whose definitions aren't demonstrably true. ~v~~
From: Lester Zick on 11 Nov 2006 15:06 On Fri, 10 Nov 2006 17:42:34 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >mueckenh(a)rz.fh-augsburg.de wrote: >> David Marcus schrieb: >> >> > WM's logic (if we can call it that) >> >> Please do not! >> You have no balls at noon. >> You have Tristram Shandy complete his diary. >> You have a diagonal longer than every line. >> You can make two balls of one. >> You have a countable model of an uncountable theory. >> >> I would be dismayed if you found any parallel between my thinking and >> your "logic". > >You need not be dismayed, since so far we haven't found any evidence >that you think at all. Look who's talking. Your thinking is no evidence one way or the other. ~v~~
From: Franziska Neugebauer on 11 Nov 2006 15:21 David Marcus wrote: > Franziska Neugebauer wrote: [...] >> So you are writing about abstract entities like functions and domains >> whereas WM does not. In WM's view a /notation/ like >> >> 1 >> 1 2 >> 1 2 3 >> ... >> >> *is* the object under consideration whereas for you it is merely an >> illustration or reference the abstract entity. > > Are you sure? If you ask him if the the above object has less than > five lines, I think he will say no. LOL. I am pretty sure that he will not agree that the above object "can have" aleph_0 lines. F. N. -- xyz
From: Lester Zick on 11 Nov 2006 15:21
On Fri, 10 Nov 2006 18:19:05 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Virgil wrote: > >> WM's problem is that he does not, perhaps cannot, understand that there >> is a difference in the way infinite sets and infinite processes work >> from the way that finite sets and finite processes work. > >I think he has a bigger problem. He doesn't seem to agree that there are >infinite sets. It is very strange. You mean if the editorial "we" agree that there are infinite sets there are infinite sets? You have a very curious sense of words in others but not in yourself. You claim to be able to prove things without being able to prove they're true. And what if one doesn't agree that there are infinite sets? Are you going to prove they're true? Clearly like most trained in the modern mathematical arts you don't take words seriously enough to form critical thoughts. ~v~~ |