Re: [Phys-l] Zero

[Brian Whatcott <betwys1@sbcglobal.net>]

Following up on Cliff's thought.

The junior school approach to division was
to imagine a pie of a size given by the numerator sliced into the number
of portions indicated by the denominator.

It seems that if you take a pie that is zero sized, perhaps call it a
non existent pie?
 and slice it not at all, the amount in each slice is ..well..unknown
as no slice of that particular pie exists!   :-)

Brian W.

At 07:25 PM 10/13/2007, you wrote:
> I like the ideas expressed in this thread. ...
> orth.  I teach high school physics.  When I ask my students to
> tell me what 0/0 or 3/0 etc. is they of course tell me that it is
> meaningless.  When I ask them why it is meaningless 90%+ can only back it up
> with because that is what my math teacher told me.  At least at the level I
> am teaching I think the question of the meaning of such quantities needs to
> be chewed on by my students more than most have chewed.
>
> Along the same lines.  A question came up the other day in class about the
> meaning of a vector of zero magnitude.  What direction is it pointing?  Can
> we really call such a thing a vector when its direction is indeterminate and
> if so why?  Because my teacher told me so doesn't count.
>
> Cliff Parker
>
> ----- Original Message -----
> From: "John SOHL" <JSOHL@weber.edu>
> To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
> Sent: Saturday, October 13, 2007 4:10 PM
> Subject: Re: [Phys-l] Zero
>
>
> > The answer is NO. But that is for the "definitive" part of your question.
> > The whole point of L'Hospital's Rule in calculus is to address the issue
> > of two functions going to zero with one of those functions divided by the
> > other. The question becomes one of "who gets to zero first."
> >
> > For example, the sinc(x) function, which is defined as sinc(x) = sin(x)/x
> > is equal to 1 when x= 0. Thus for x=0 you have the case which you
> > describe:
> > sin(x)/x = sin(0)/0 = 0/0 and the answer is 1 by L'Hospital's Rule.
> >
> > The sinc(x) function is very common in optics when calculating diffraction
> > patterns for slits.
> >
> > In general there is no fixed or "definitive" answer for 0/0, you must know
> > how you have approached that point.
> >
> > Other functions for 0/0 will reach other values including zero and
> > infinity. In the end, L'Hospital's Rule, rules! :-)
> >
> > John
> >
> > - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
> > John E. Sohl, Ph.D.
> > Professor of Physics
> > Weber State University
> > 2508 University Circle
> > Ogden, UT 84408-2508
> >
> > voice: (801) 626-7907, fax: (801) 626-7445
> > e-mail: jsohl@weber.edu
> > web: http://physics.weber.edu/sohl/
> >
> >>>> JMGreen <jmgreen@sisna.com> 10/12/2007 4:19 PM >>>
> > Has the fraction zero/zero a definitive answer?
> >
> > Is there a book named "Zero" which purports a definitive answer?
> >
> > Jim
> >
> > J M Green
> > Email:  MailTo:JMGreen@sisna.com
> > WWW: http://users.sisna.com/JMGreen
> >
> >
> > _______________________________________________
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>
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Brian Whatcott    Altus OK    Eureka!