Cantor Confusion
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From: David Marcus on 9 Dec 2006 03:13 Eckard Blumschein wrote: > On 12/7/2006 7:06 PM, Lester Zick wrote: > > On Thu, 7 Dec 2006 02:04:34 -0500, David Marcus > > <DavidMarcus(a)alumdotmit.edu> wrote: > >>Bob Kolker wrote: > >>> Eckard Blumschein wrote: > >>> > >>> > Roughly speaking, it just claims that a set is unambiguously determined > >>> > by its elements. If i recall correctly A=B<-->(A in B and B in A) > >>> > > >>> > Perhaps the Delphi oracle provided less possibilities of tweaked > >>> > interpretation betwixed and between potential and actual infinity. > >>> > >>> What is "potential" infinity. Can you define it rigorously? > >> > >>Even a non-rigorous defintion would be a start. > > > > Well since according to David a definition is "only an abbreviation" > > how about "X"? > > Strictly speaking there is no potential infinity. Infinity is a > fictitious quality. The series of natural numbers is potentially > infinite. Aristotele wrote: Infinity exists potentially. There is no > actual infinity. > > Marcus is quite right. We should better explain such basic terminology. You appear to have just said that there is no "potential infinity" and no "actual infinity". Is this correct? If so, why do you keep using the phrases??? And, what in the world have you been talking about all this time? Nothing? Sheesh. At least make an effort. -- David Marcus
From: David Marcus on 9 Dec 2006 03:16 Eckard Blumschein wrote: > On 12/7/2006 8:38 AM, Virgil wrote: > > In article <MPG.1fe18bc534a955549899ed(a)news.rcn.com>, > > David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > > >> Eckard Blumschein wrote: > >> > >> > I didn't find a single counter-example. > >> > >> That doesn't prove anything. In mathematics, we prove things. > > Who proved Cantor's interpretation of his second diagonal argument? << lots snipped >> Just for fun, let's try to discuss one thing at a time, and go one step at a time. Cantor's theorem is that there is no surjection from the natural numbers to the reals. Do you agree that this is the statement of the theorem? -- David Marcus
From: David Marcus on 9 Dec 2006 03:18 Eckard Blumschein wrote: > On 12/7/2006 8:24 AM, David Marcus wrote: > > Eckard Blumschein wrote: > > >> Why do you not admit the possibility that countability of > >> a set requires countable numbers. Doesn't it make sense? > > > > Of course, it doesn't make sense. The reasons are: > > > > 1. You haven't defined/explained what a "countable number" is. > > Countability is self explaining. Nonsense. If you use a word, you must define it. Please define "countable number". -- David Marcus
From: David Marcus on 9 Dec 2006 03:25 Eckard Blumschein wrote: > On 12/7/2006 8:18 AM, David Marcus wrote: > > Eckard Blumschein wrote: > >> On 12/5/2006 2:13 PM, Bob Kolker wrote: > >> > For the latest time. Uncountability is a property of sets, not > >> > individual numbers. > >> > >> I know this widespread view. > > > > So you claim. However, last time I asked you to give the standard > > definitions, you failed. Care to try again? Define "countable" and > > "uncountable". > > Do you believe someone who is urged to say the words of pater noster ... > will immediately become a believer? Irrelevant. You said you knew standard mathematics. So, I asked you to show us. It is a perfectly reasonable request. If you really know any, you should have no trouble convincing us. However, you have frequently given the impression that you are very unfamiliar with standard mathematics. While it is possible to have an opinion about music without knowing how to play an instrument, it really isn't possible to have a sound opinion about mathematics without knowing some mathematics. > >> Real numbers according to DA2 are uncountable altogether. People like > >> you will not grasp that. > > > > And, people like you don't listen when we point out that "DA2" does not > > define/construct/characterize the real numbers. > > O.K. I agree. Cantor had first to chose an appropriate definition and > then to make sure that it was fulfilled in his DA2. Thanks. -- David Marcus
From: David Marcus on 9 Dec 2006 03:29
Virgil wrote: > In article <4579B665.9010009(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > On 12/7/2006 7:54 AM, David Marcus wrote: > > > Eckard Blumschein wrote: > > > >> Notice: Cantor's untennable definition > > > > > > Which definition are you referring to? > > > > See an other reply of mine today. > > None of those relies describe any definition by Cantor that is > mathematically or logically untenable. > > So one must conclude that EB is faking it. Yes, I couldn't find any statement of the untenable definition either, and I think I've read all the posts. I suppose EB really believes he posted it. Oh, well. EB, please post it again and clearly label it. -- David Marcus |