Galileo's Paradox
in [Math]
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From: Virgil on 5 Dec 2006 18:06 In article <4575B119.2050709(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/4/2006 11:32 AM, Bob Kolker wrote: > > Eckard Blumschein wrote: > > > >> Notice, there is not even a valid definition of a set which includes > >> infinite sets. Cantor's definition has been declared untennable for > >> decades. > > > > That is simply not so. For example the set of integers. There is is. > > Perhaps, you are honestly bold. Believe me that Fraenkel admitted that > Cantor's definition is untennable. So Fraenkel is wrong! > The question is e.g. in case of the > naturals whether they are considered one by one or altogether like an > entity. While a set is usually imagined like something set for good, > this point of view is unrealistic. It is essential. And since all numbers are unrealistic in that they are only imagined, that is no handicap.
From: Virgil on 5 Dec 2006 18:08 In article <4575B16C.6050508(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/4/2006 9:47 AM, Virgil wrote: > > In article <4573D4DA.4040709(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > > >> On 12/3/2006 8:22 PM, cbrown(a)cbrownsystems.com wrote: > >> > Tony Orlow wrote: > >> > > >> > Well, you used the term "set" four times in your above definition of > >> > what we mean by a "set". That's why I said "this begs the question, > >> > what do we mean, exactly, by a set of properties?". > >> > > >> > There's something that we intuitively seem to think of as a "set"; but > >> > unless such a thing is carefully defined, we end up with the > >> > contradictions of naive set theory: > >> > > >> > http://en.wikipedia.org/wiki/Naive_set_theory > >> > >> Is it really justified to blame an allegedly insufficient definition of > >> the term set for obvious antinomies of set theory? > > > > > > As "set" and "is a member of" are primitives in axiomatic set theory, > > any "definition" of them is outside of set theory and irrelevant to it. > > Yes. The problems are shifted outside. Nothing outside of an axiom system can be a problem inside that system. That is the point of axiom systems. So as soon as one has ZF or NBG, all EB's alleged problems go away.
From: Virgil on 5 Dec 2006 18:11 In article <4575B842.70801(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/5/2006 4:01 PM, Bob Kolker wrote: > > Eckard Blumschein wrote: > >> > >> > >> Those who declared Cantor naive overlooked Dedekind. Learn German and > >> enjoy his childish innocent style. > > > > He also gave a correct definition for the real numbers, too. > > I explained why I am objecting against his claims. > > > > > There are other definitions which are equivalent. > > Yes. They are equally imprecise. > > > For example using > > limit points of Cauchy sequences > > I would agree if you did add the original word "fictitious" to these > sequences. > > of rational numbers which is the > > topological closure of the rational number space with interval topology > > and the usual metric. > > > > Bob Kolker > > Please do no longer keep me for as ignorant as you seems to be. As long as you keep corroborating our opinions of your ignorance, we shall continue to hold and express them.
From: Virgil on 5 Dec 2006 18:12 In article <4575BAD0.8020701(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/5/2006 4:46 PM, Tonico wrote: > > Eckard Blumschein ha escrito: > > > >> On 12/4/2006 11:52 PM, Virgil wrote: > >> > >> >> I am an electrical engineer > >> > > >> > Shocking! > >> > >> Why? We love mathematics. > > *************************************************** > > Oh, I bet elec. eng. love maths; the problem seems to be that maths > > does not correspond AT ALL that love, at least in the case of several > > engineers...**sigh**...tough. > > Tonio > > > What is maths? The eastpondian version of math.
From: cbrown on 5 Dec 2006 20:03
Lester Zick wrote: > On 4 Dec 2006 17:57:54 -0800, cbrown(a)cbrownsystems.com wrote: > > > > >Lester Zick wrote: > >> On 4 Dec 2006 11:29:33 -0800, cbrown(a)cbrownsystems.com wrote: > >> > >> > > >> >Lester Zick wrote: > >> >> On 3 Dec 2006 11:22:56 -0800, cbrown(a)cbrownsystems.com wrote: > >> >> > >> >Of course it doesn't; "all of mathematics" is an extremely broad range > >> >of discourse. > >> > >> So when mathematikers conflate mathematical ignorance with set > >> "theory" ignorance they are being extremely overly broad? > >> > > > >Not all of Italian cooking involves sauteeing things in olive oil; > >however it is somewhat bizzare for someone to claim to be a > >knowledgeable Italian cook without knowing how to sautee things in > >olive oil. > > Then you undoubtedly qualify as an Italian cook and set mathematiker > in your spare time. I'm just trying to ascertain the basis for your > disdain of Italian cooks who don't choose to practice what you preach. > Why do you assume that I disdain cooks (Italian or otherwise) who don't know how to sautee things in olive oil? I simply think that it's bizzare to claim to be a knowledgable Italian cook, when one cannot sautee things in olive oil. I doubt such a person get a job at an Italian restaurant. Cheers - Chas |