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Re: [Phys-l] Zero



I understand "operational definition" of physical terms. I do not understand the difference in mathematics between a "definition" and an "operational definition".
As for the troublesome and hard-to-undeerstand concept of limits,
that concept was made unnecessary in the '50's by the non-standard analysis of Abraham Robinson, used in my Calculus Text (in progress). Chapter III inttroduces the "dibble', somewhat whimsically defined as a quantity so small that its square is zero (well, as godd as zero, and if it is as good as zero why not call it zero - see the Mikado for the logic) and which is eventually written "dx" (Lou Kaufman, the "knot" man at UIC told me that he does something similar in his calculus course). The dibble approach can be made rigorous by invoking Robinson's infinitesimals, but these are theoretical embellishments that I decline to inflict on students (although others have).
Neither Newton nor Leibniz recognized a theory of limits,
Conclusion: 0/0 is meaningless.
Regards,
Jack
p.s. Chapter III is separately available on my website at
http://www.hep.anl.gov/jlu/index.html

On Sat, 13 Oct 2007, Bob Sciamanda wrote:

| Has the fraction zero/zero a definitive answer?

The answer of course hinges on your operational definition of the
division operation a/b, including the requirements which this
definition might impose upon the mathematical entities a and b.

I would submit that by conventional definitions, 0/0 is meaningless.
One is however persuaded to define a new, useful, related concept :
The limiting value of f(x)/g(x) as both f(x) and g(x) approach the
value 0 for some value of x. ( This also may be meaningless in
particular instances.)

Bob Sciamanda
Physics, Edinboro Univ of PA (Emeritus)
www.winbeam.com/~trebor
trebor@winbeam.com
----- Original Message -----
From: "JMGreen" <jmgreen@sisna.com>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Friday, October 12, 2007 6:19 PM
Subject: [Phys-l] Zero


| 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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