I to was and am a bit puzzled. To me "any C-vector" means "any and all"
or equivalently for "arbitrary C-vector"
Is the objection merely to the word "cancel"?
Admittedly its not cancelation in the sense of dividing both sides by
the C-vector. But this reasoning gets used all the time for equating
coefficients to arbitrary quantities. The key is realizing that its not
cancelation in the sense operating with the inverse on both sides of the
equation.
Or am I missing something?
________________________
Joel Rauber
Department of Physics - SDSU
Joel.Rauber@sdstate.edu
605-688-4293
| -----Original Message-----
| From: Forum for Physics Educators
| [mailto:PHYS-L@list1.ucc.nau.edu] On Behalf Of Bob Sciamanda
| Sent: Thursday, February 09, 2006 9:44 AM
| To: PHYS-L@LISTS.NAU.EDU
| Subject: Re: Elecric Field Lines
|
| John,
| On second thought, I see your point - even granting the
| inference "any and all Cvectors"- that this is not a
| canceling operation.
| It is one of those liberties which we take with mathematical
| rigor, as eg; replacing (ds/dt)*dt with ds and calling it
| "canceling" the dt.
|
| There is a justifying logic, but "canceling" is not the
| proper word for it.
|
| Bob Sciamanda
| Physics, Edinboro Univ of PA (Em)
| http://www.winbeam.com/~trebor/
| trebor@winbeam.com
| ----- Original Message -----
| From: "Bob Sciamanda" <trebor@WINBEAM.COM>
| To: <PHYS-L@LISTS.NAU.EDU>
| Sent: Thursday, February 09, 2006 10:31 AM
| Subject: Re: Elecric Field Lines
|
|
| | JM wrote:
| || . . .
| || Just yesterday I had every student in a junior E and M
| class tell me
| || that, if Cvector dot Avector = Cvector dot Bvector for any Cvector
| || then we can cancel the Cvector on both sides of the equation and
| || determine that Avector = Bvector. That is the right
| answer, and the
| || argument is appealing, but it is, nevertheless, wrong.
| || . . .
| |
| | Perhaps they were inferring "for any Cvector" to mean "for
| any and all
| | possible Cvectors"
| |
| | Bob Sciamanda
| | Physics, Edinboro Univ of PA (Em)
| | http://www.winbeam.com/~trebor/
| | trebor@winbeam.com
| |
|
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