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Re: [Phys-l] Zero

Hi all-
But the mantra "L'Hospial's rule" is not an answer to the question, any more than the simple answer, "No". In fact. if I define
sinc(x) = sine(x)/x, without more, sinc(0)= 1 is not necessarily correct.
It is only correct for a particular choice of units for x.
Regards,
Jack



On Sat, 13 Oct 2007, Cliff Parker wrote:

I like the ideas expressed in this thread. I hope you will allow me to add
my two cents worth. 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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