Cantor Confusion
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From: David Marcus on 9 Dec 2006 02:47 Han de Bruijn wrote: > David Marcus wrote: > > > That makes sense. And, most people have no understanding of the function > > concept, so they don't see its utility or pervasiveness. > > Huh? Most people, especially the people who work with their hands, have > a much better understanding of the function concept than you may think! > > An example. What is the best way to disassemble a device and assemble it > again? (For example if you need to clean the parts or repair something) > > Take a big towel. Take the parts out of the device and put them on the > towel in the same order as you have taken them out. After you have done > your thing, put the parts back into the device, but now in the _reverse_ > order as you have taken them out: last out, first in. The above is quite > common practice among i.e. metal workers. The mathematical background of > this is the formula for the inverse of a composed function: > > (A.B.C.D.E.F.G.H.K.L)^(-1) = > L^(-1).K^(-1).H^(-1).G^(-1).F^(-1).E^(-1).D^(-1).C^(-1).B^(-1).A^(-1) > > Maybe they don't know it with their minds, but they _do_ it with their > hands. My own conclusion has been: show some respect for "most people" ! Well, that's a pretty odd example to give of the function concept. Looks more like a nonabelian group or tracing a path in a graph. Regardless, I certainly have more respect for most people than I do for you, especially after reading the above. -- David Marcus
From: David Marcus on 9 Dec 2006 02:58 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. -- David Marcus
From: David Marcus on 9 Dec 2006 03:00 Eckard Blumschein wrote: > On 12/7/2006 9:58 PM, Virgil wrote: > > According to EB, who confesses that he is not a mathematician. > > Nonetheless I can read and reason. Please demonstrate that you can "read and reason": State a theorem and give its proof. -- David Marcus
From: David Marcus on 9 Dec 2006 03:07 Eckard Blumschein wrote: > On 12/7/2006 7:07 PM, Lester Zick wrote: > > On Thu, 7 Dec 2006 02:18:36 -0500, David Marcus > > <DavidMarcus(a)alumdotmit.edu> 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". > > > > Since according to you "definitions are only abbreviations" how about > > def(countable)="Y" and def(uncountable)="Z"? > > > > ~v~~ > > David expects from me a confession of faith. Sorry. No. I'm just looking for any mathematics. This is sci.math, after all. You post an incredible amount of stuff, but it doesn't seem to contain any actual math. Mostly lots of claims about what various dead people supposedly believed. Kind of boring. How about a simple statement of some math? -- David Marcus
From: David Marcus on 9 Dec 2006 03:10
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. > 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. -- David Marcus |