On Mon, 10 May 2004 15:56:10 +0000 (UTC), email@example.com (James Dolan) wrote:
>in article <firstname.lastname@example.org>, >david c. ullrich <email@example.com> wrote: > >|On Sun, 9 May 2004 20:43:01 +0000 (UTC), >|firstname.lastname@example.org (James Dolan) wrote: >| >|>in article <email@example.com>, >|>dave rusin <firstname.lastname@example.org> wrote: >|> >|>|>> The student should be able to give a rendition that is at least >|>|>> equivalent to the one given in the book and that uses precise language. >|>|> >|>|> Let me try that one...independence means a group of vectors (in >|>|> homogenous form???) such that if they all equal the zero vector, then >|>|> the only possible way for that is the each coefficient of every vector >|>|> has to equal 0 too. >|>| >|>|OK, now, jdolan and others who pooh-poohed the idea of memorizing >|>|definitions: what say you to this student? Seems to me he has >|>|made my point for me ... >|> >|> >|>hi dave. i've been too busy to keep up with this thread lately, but i >|>happened to glance at the new "linear algebra definitions" thread that >|>the student in question started a couple of days ago, and it looks >|>like he has unmade your point for you. >|> >|>anyway, i think it does students a great disservice to conflate the >|>very important ability to engage in precise reasoning with the >|>completely unimportant ability to memorize definitions. >| >|And you _really_ think that if he's saying things like "independence >|means a group of vectors (in homogenous form???) such that if they >|all equal the zero vector, then the only possible way for that is >|the each coefficient of every vector has to equal 0 too" he's >|going to be able to engage in precise reasoning about independence? > >presumably if i thought that then i would have said something remotely >like it. i'll take the fact that you're spewing nonsense like this >now as your concession that you've lost the argument.
Uh, you don't seem to be making much sense - from your last two posts it appears that you agree that each of the following statements is correct:
(i) the ability to engage in precise reasoning is very important. (ii) the ability to memorize definitions is relatively unimportant. (iii) someone whose notion of a certain definition is as above will not be able to engage in precise reasoning.
Those three statements seem mutually inconsistent.
I imagine I'm missing something. Which part of what you've said am I misinterpreting?