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BURT
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 Posted: Sun Jun 29, 2008 2:56 am Post subject: The Two Infinitesimals Zero and Nonzero infinitely small |
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For polynomial functions the infinitesimal is a zero dimensional point
and derivatives are exact. For real world curves the infinitesimal is
two points infinitely close. We can only calculate an approximation of
the infinitely close therefore our answers for real world curves
always remains an approximation. The more calculations we do the
closer our answer will be but never quite reaching exactitude.
Mitch Raemsch |
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Darwin123
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| Posted: Mon Jun 30, 2008 1:06 am Post subject: Re: The Two Infinitesimals Zero and Nonzero infinitely small |
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On Jun 28, 10:56 pm, BURT <macromi...@yahoo.com> wrote:
| Quote: |
For polynomial functions the infinitesimal is a zero dimensional point
and derivatives are exact. For real world curves the infinitesimal is
two points infinitely close. We can only calculate an approximation of
the infinitely close therefore our answers for real world curves
always remains an approximation. The more calculations we do the
closer our answer will be but never quite reaching exactitude.
Mitch Raemsch
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Look up the rules for significant figures. Also look up error
analysis. Then look at differentials again. In the real world,
differential mathematics works because the error is in those
significant figures we lop off. Differential mathematics represents an
abstract way to approach round off error. |
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BURT
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| Posted: Mon Jun 30, 2008 1:40 am Post subject: Re: The Two Infinitesimals Zero and Nonzero infinitely small |
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On Jun 29, 5:06 pm, Darwin123 <drosen0...@yahoo.com> wrote:
| Quote: |
On Jun 28, 10:56 pm, BURT <macromi...@yahoo.com> wrote:
For polynomial functions the infinitesimal is a zero dimensional point
and derivatives are exact. For real world curves the infinitesimal is
two points infinitely close. We can only calculate an approximation of
the infinitely close therefore our answers for real world curves
always remains an approximation. The more calculations we do the
closer our answer will be but never quite reaching exactitude.
Mitch Raemsch
Look up the rules for significant figures. Also look up error
analysis. Then look at differentials again. In the real world,
differential mathematics works because the error is in those
significant figures we lop off. Differential mathematics represents an
abstract way to approach round off error.
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That is an excuse. Calculus in the cases I speak of or real world
curves is never exact.
Mitch Raemsch |
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Robert J. Kolker
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| Posted: Mon Jun 30, 2008 3:22 am Post subject: Re: The Two Infinitesimals Zero and Nonzero infinitely small |
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mitch.nicolas.raemsch@gmail.com wrote:
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Abstract entities.
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So are the numbers you use for your bank account.
Bob Kolker |
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David R Tribble
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| Posted: Tue Jul 01, 2008 3:50 am Post subject: Re: The Two Infinitesimals Zero and Nonzero infinitely small |
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BURT wrote:
| Quote: |
For polynomial functions the infinitesimal is a zero dimensional point
and derivatives are exact. For real world curves the infinitesimal is
two points infinitely close. We can only calculate an approximation of
the infinitely close therefore our answers for real world curves
always remains an approximation.
|
What is a "real-world curve"? Is it similar to a "mathematical
curve"? |
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Guest
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| Posted: Tue Jul 01, 2008 3:56 am Post subject: Re: The Two Infinitesimals Zero and Nonzero infinitely small |
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On Jun 30, 7:50 pm, David R Tribble <da...@tribble.com> wrote:
| Quote: |
BURT wrote:
For polynomial functions the infinitesimal is a zero dimensional point
and derivatives are exact. For real world curves the infinitesimal is
two points infinitely close. We can only calculate an approximation of
the infinitely close therefore our answers for real world curves
always remains an approximation.
What is a "real-world curve"? Is it similar to a "mathematical
curve"?
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Changes in the real world quantities described by a changing curve.
Mitch Raemsch |
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Mad Ape
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| Posted: Tue Jul 01, 2008 5:19 am Post subject: Re: The Two Infinitesimals Zero and Nonzero infinitely small |
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BURT wrote:
| Quote: |
For polynomial functions the infinitesimal is a zero dimensional point
and derivatives are exact. For real world curves the infinitesimal is
two points infinitely close. We can only calculate an approximation of
the infinitely close therefore our answers for real world curves
always remains an approximation. The more calculations we do the
closer our answer will be but never quite reaching exactitude.
Mitch Raemsch
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Infinity + 1 = Infinity
1 = Infinity - Infinity
1 = 0
The Mad Ape
www.tatumba.com |
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Spaceman
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| Posted: Tue Jul 01, 2008 5:35 am Post subject: Re: The Two Infinitesimals Zero and Nonzero infinitely small |
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Mad Ape wrote:
| Quote: |
BURT wrote:
For polynomial functions the infinitesimal is a zero dimensional
point and derivatives are exact. For real world curves the
infinitesimal is two points infinitely close. We can only calculate
an approximation of the infinitely close therefore our answers for
real world curves always remains an approximation. The more
calculations we do the closer our answer will be but never quite
reaching exactitude.
Mitch Raemsch
Infinity + 1 = Infinity
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Nope,
Infinity = I
I + 1 = I +1
no matter what you do.
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1 = Infinity - Infinity
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Nope.
0 = infinity - infinity
--
James M Driscoll Jr
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Guest
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| Posted: Fri Jul 04, 2008 2:05 am Post subject: Re: The Two Infinitesimals Zero and Nonzero infinitely small |
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On Jun 29, 2:22 pm, "Robert J. Kolker" <bobkol...@comcast.net> wrote:
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mitch.nicolas.raem...@gmail.com wrote:
Abstract entities.
So are the numbers you use for your bank account.
Bob Kolker
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Right. But that has nothing to do with the abstract entities used in
calculus: the infinitely small zero and nonzero infinitesimal. One
abstract entity does not apply to the real world and the approximation
of another does. |
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