Cantor Confusion
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From: Lester Zick on 9 Dec 2006 12:36 On Sat, 9 Dec 2006 02:58:42 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Eckard Blumschein wrote: >> On 12/8/2006 1:05 AM, David Marcus wrote: >> > Eckard Blumschein wrote: >> >> On 12/5/2006 9:23 PM, Virgil wrote: >> >> >> >> >> Do not confuse Cantor's virtue of belief in god given sets with my power >> >> >> of abstraction. >> >> > >> >> > Cantor's religious beliefs are as irrelevant as EB's beliefs in his own >> >> > infallibility. >> >> >> >> I am not infallible. Show me my errors, and I will express my gratitude. >> > >> > Show you your errors or convince you that they really are errors? The >> > former is simple, but the latter appears to be impossible. We can't >> > force you to learn, if you don't wish to. >> >> I can force you to either refute e.g. my hint that Cantor's definition >> of a set has been declared untenable or tacitly accept this fact. > >Please restate the definition that you say is untenable. Let's take a >look. How can an abbreviation be untenable? ~v~~
From: Lester Zick on 9 Dec 2006 13:00 On Sat, 9 Dec 2006 00:01:47 GMT, "Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote: >In article <5pejn2d7ekq7stdqbp8cg31ukse5mlnka6(a)4ax.com> Lester Zick <dontbother(a)nowhere.net> writes: >... > > Of course. I was just mocking David's idiotic definition of definition > > as only an abbreviation which he doesn't seem particularly anxious to > > defend. > >I suppose you did not understand him (as you do not understand many people). Naturally I don't understand David just as I don't understand many people including you. His words however are a different matter. No particular mystery there. His words are quite clear. I understand them quite well. David said definitions are only abbreviations. He asked for a definition so I gave him an abbreviation. End of report. >A definition provides a short term for a long sentence, or even more than >a single sentence. Is this your own private definition for a definition? Where does what you say indicate a definition is only an abbreviation? > That is when I write: > Let N be the set of natural numbers >that is a definition of N as a short-hand for "the set of natural numbers". So what? "N" is an abbreviation. "N is the set of natural numbers" is not "only an abbreviation". If I were trying to understand you I would be inclined to ask "Could you possibly be as stupid as you pretend"? >Note also *what* is defined here: N. So when somebody asks for a >definition of "protential infinite" the question is for a long description >of what that is. No. What David asked for was only an abbreviation because he asked for a definition and he claimss a definition is only an abbreviation. Now we all understand this isn't true but then according to David definitions aren't true either. So no special problem there. I gave him what his words asked for. I can't help it if you and David don't understand his own words. But that's undoubtedly what happens when mathematikers try to talk out of both sides of their mouths at the same time. But then I'm sure you understand David much better than I. ~v~~
From: Lester Zick on 9 Dec 2006 13:13 On Sat, 9 Dec 2006 03:10:38 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Dik T. Winter wrote: >> In article <5pejn2d7ekq7stdqbp8cg31ukse5mlnka6(a)4ax.com> Lester Zick <dontbother(a)nowhere.net> writes: >> ... >> > Of course. I was just mocking David's idiotic definition of definition >> > as only an abbreviation which he doesn't seem particularly anxious to >> > defend. >> >> I suppose you did not understand him (as you do not understand many people). > >I doubt Lester even tried to understand. I have no interest in understanding you, David. Your words however are a different matter. They're quite clear. You maintain definitions are only abbreviations. Your words asked for a definition so I gave you an abbreviation. End of report. >> A definition provides a short term for a long sentence, or even more than >> a single sentence. That is when I write: >> Let N be the set of natural numbers >> that is a definition of N as a short-hand for "the set of natural numbers". >> Note also *what* is defined here: N. So when somebody asks for a >> definition of "protential infinite" the question is for a long description >> of what that is. > >Quite clear. But, I doubt Lester will understand you any better than >he's understood other people. I don't try to understand you, David. Shrinks get paid good money for understanding people. I try to confine myself to understanding their words. Your words said definitions are only abbreviations. Now we all understand that isn't true but then you maintain definitions aren't true either. So I gave you what your words asked for: an abbreviation. What's your problem? I realize it's hard to maintain synchronization for words coming out of both sides of your mouth at the same time, but that seems to be a chronic psychological disorder among mathematikers. So do try to keep up. ~v~~
From: David Marcus on 9 Dec 2006 14:03 Bob Kolker wrote: > David Marcus wrote: > > > Nonsense. If you use a word, you must define it. Please define > > "countable number". > > Not every word can be (verbally) defined. This would lead to > circularity. Some words can only be defined by ostention or example. Or, by giving axioms that the word satisfies. However, something must be given or we are only discussing poetry. -- David Marcus
From: David Marcus on 9 Dec 2006 14:05
Lester Zick wrote: > On Sat, 9 Dec 2006 02:58:42 -0500, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > > >Eckard Blumschein wrote: > >> On 12/8/2006 1:05 AM, David Marcus wrote: > >> > Eckard Blumschein wrote: > >> >> On 12/5/2006 9:23 PM, Virgil wrote: > >> >> > >> >> >> Do not confuse Cantor's virtue of belief in god given sets with my power > >> >> >> of abstraction. > >> >> > > >> >> > Cantor's religious beliefs are as irrelevant as EB's beliefs in his own > >> >> > infallibility. > >> >> > >> >> I am not infallible. Show me my errors, and I will express my gratitude. > >> > > >> > Show you your errors or convince you that they really are errors? The > >> > former is simple, but the latter appears to be impossible. We can't > >> > force you to learn, if you don't wish to. > >> > >> I can force you to either refute e.g. my hint that Cantor's definition > >> of a set has been declared untenable or tacitly accept this fact. > > > >Please restate the definition that you say is untenable. Let's take a > >look. > > How can an abbreviation be untenable? Why ask me? EB is the one who said it. -- David Marcus |