Cantor Confusion
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From: Lester Zick on 31 Oct 2006 18:32 On Tue, 31 Oct 2006 02:16:29 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >imaginatorium(a)despammed.com wrote: >> David Marcus wrote: >> > Lester Zick wrote: >> > > On Mon, 30 Oct 2006 16:43:03 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >> > > >Han de Bruijn wrote: >> > > >> David Marcus wrote: >> > > >> > Han.deBruijn(a)DTO.TUDelft.NL wrote: >> > >> > > >> >>And add this to the fact that noon and beyond cannot exist >> > > >> >>in this problem. >> > > >> > >> > > >> > Are you still doing physics, water, and a finite number of molecules? >> > > >> > Let us know when you switch to mathematics. >> > > >> >> > > >> I'm DOING mathematics. Mathematics is NOT independent of Physics. >> > > > >> > > >I guess your definition of "mathematics" is different from mine. >> > > >> > > I think the only relevant question is whether your definition of >> > > "mathematics" is demonstrably true? If not I don't see that any >> > > definition of mathematics is more virtuous one way or the other. >> > >> > That would depend on what your definition of "demonstrably true" is. My >> > definition of "mathematics" agrees with what mathematicians do. >> > >> > Is it "demonstrably true" that "noon... cannot exist"? >> >> Be careful not to mix up your interlocutors - this is Lester, and I >> expect he will only be interested in whether noon is true or not. > >I think I realized that Lester was commenting on something I said to >Han, and I was asking Lester (just out of idle curiosity) if he thought >that Han's idea of "mathematics" satisfied Lester's criterion. If not demonstrably true anything you have to say is just so much idle curiosity. >I wonder: do Lester, Ross, Han, Tony, and WM all agree that noon doesn't >exist? I think it more likely that you don't exist. > It is such an odd thing to say. Imagine walking up to someone in >the street and trying to convince them that noon doesn't exist. No harder than trying to convince them that you're true. >It is so hard to keep the nonsense straight. Just not quite as difficult to keep your nonsense straight. > It all seems to run >together--although there are stylistic differences. An insistence that >words mean whatever the writer wants them to mean (if they mean anything >at all) seems to underly most of the poetry. Ah there is goes. Sucking up to Brian. Trying to build some kind of power base. The politics of neomathematics. If you can't deal with truth deal with power instead. The perfect model of a neomathematiker. ~v~~
From: Lester Zick on 31 Oct 2006 18:33 On 31 Oct 2006 06:42:17 -0800, imaginatorium(a)despammed.com wrote: > >David Marcus wrote: > ><snip> > >> I wonder: do Lester, Ross, Han, Tony, and WM all agree that noon doesn't >> exist? It is such an odd thing to say. Imagine walking up to someone in >> the street and trying to convince them that noon doesn't exist. >> >> It is so hard to keep the nonsense straight. It all seems to run >> together--although there are stylistic differences. > >More than stylistic, I think. For example, don't offhand recall Lester >ever saying anything mathematical that was even wrong, whereas our Tony >is reponding in another thread, saying something that makes sense, >seems to be correct, and (gasp!) includes use of the f-word. Yes, yes, oh zenboy extraordinaire. But have you ever said anything that was demonstrably true? ~v~~
From: David Bernier on 31 Oct 2006 18:35 William Hughes wrote: [...] > You miss the point. The point is not whether an infinite set exists or > not. > The point is that it is possible to define the properties that > an infinite set must satisfy, without answering the questions > "does an infinite set exist". Similarly, I can say "A unicorn is a > horse > like creature with a white horn in its forehead", without having to > decide whether or not unicorns exist. We can say that the definition > of unicorn exists, even if no unicorn exists, and thus it > makes sense to talk about the definition. (An interesting question is: > "Under the assumption that unicorns do not exist, does the question > "Does a unicorn have a white horn?" make sense?" > (I would say yes, and that furthermore, one correct answer to the > question > is no.)) Hypothesis: "Unicorns do not exist" Claim: "Every unicorn has 666 eyes". Proof: "Every unicorn has 666 eyes" is vacuously true, since there are no unicorns under the hypothesis. Are there other (sensible, arguable) ways to interpret or answer your question "Under the assumption that unicorns do not exist, does the question "Does a unicorn have a white horn?" make sense?" ? I ask you this since I have a medium belief that you study philosophy. David Bernier
From: Lester Zick on 31 Oct 2006 18:36 On Mon, 30 Oct 2006 21:55:45 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Dik T. Winter wrote: >> In article <md5ak294kscg4uk48a276jktc64lf430rq(a)4ax.com> Lester Zick <dontbother(a)nowhere.net> writes: > >> > Whereas if I try to define the quaity of infinity in specific objects >> > as in "infinity(x) is . . ." I'm stuck with whatever x may turnout to >> > be and without specifying what x is there is no way to determine >> > whether the definition can be correct or not. >> >> This is wrong. You do not define the quality of infinity in specific >> objects, but as a general property within a set of axioms (part of your >> domain of discourse). As far as I know, "infinity" in mathematics has >> only been defined in the context of topology, where it is the single point >> used in the one-point compactification (but it is long ago that I did all >> this). And from there it has a derived definitions in projective geometry >> (the point at infinity, and also the line at infinity). The term is used, >> losely, in analysis, using limits, but is not really defined there as term. >> You will see oo used in analysis, but when it is used it does *not* mean >> "infinity". When that symbol is used the usage has a specific definition. > >I believe it is quite common in analysis to use the "extended real >numbers". The extended real numbers is R with the addition of two >elements +oo and -oo. E.g., see the book "Real Analysis" by H.L. Royden. It may be quite common but is it true? >> > >The same holds for the Godbach conjecture. When you read current accounts, >> > >they are clear, but when you read the original, it is nonsense. Until you >> > >realise that the original was written when 1 was considered to be prime. >> > >According to the tables of D. H. Lehmer, there are five primes smaller >> > >than 10. >> > >> > But don't forget the process of comprehension itself improves vastly >> > with time and experience of expression. When I look back over my own >> > posts the level and sophistication of expression and application has >> > improved enormously. >> >> No, there is something else. In time definitions in a particular field >> of mathematics can change over time. So when you are reading old books >> or articles you need to know whether the definitions actually have been >> changed since then or not. Especially Wolfgang Mueckenheim does not >> allow for such changes of definitions. > >WM doesn't seem to even understand what the old books or articles meant >when they were written. Whereas you understand what they meant but not whether they were true past or present. ~v~~
From: MoeBlee on 31 Oct 2006 18:48
Lester Zick wrote: > On 30 Oct 2006 15:21:01 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > > >Lester Zick wrote: > >> My mistake, Moe. It's just that you keep snipping all these posts. > > > >I snip so that the posts are not ridiculously long. If I ever leave out > >context that you feel needs to be included, then you may reinstate that > >context in your reply. I do not snip to materially distort context, > >though I recognize that even judicious snipping by its very nature > >omits context that, in some aspect, may be considered needed. > > Well if I previously indicated that converstations with you were short > and to the point, I plead guilty but didn't imagine that was a license > to truncate and then complain about what was said in the material > truncated. Otherwise I have no intention of trying to reconstruct the > conversation or arguing the subject further especially since David has > taken to whining about it in your behalf. > > >I disagree strongly with many things you say, but of course I do not > >begrudge your prerogative to say whatever you like about these subjects > >as I reply and say what I disagree with in what you've said (which is > >not generous of me, but rather is, to me, just a reflection of the > >basic premise that everyone gets to speak his or her mind)...except I > >ask you please not to claim I've said things that I have not said > >through your incorrect paraphrases of what I said. > > I don't recall quoting you directly and literally but of extrapolating > the implications of what you said whether you agree with those > implications and my inferences or not. The problem I noted directly > concerned your ideas and claims of standard mathematical definition > which were not employed by Stephen. If I were to reply in Zickian fashion, it would be "Who cares?" (Moderate language version.) Anyway, since you ARE going on about this still, it's not a matter of your "extrapolating implications" but of your intentionally mangling the formulas and making it look as if your mangled versions were what I was claiming and also saying that I said certain things that are NOT plausible "extrapolations of what I said". MoeBlee |