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Re: Re: Question about Replace

• To: mathgroup at smc.vnet.net
• Subject: [mg35762] Re: [mg35753] Re: Question about Replace
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Tue, 30 Jul 2002 07:22:11 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

  That should have been Leibniz, of course.

On Monday, July 29, 2002, at 05:15  PM, Andrzej Kozlowski wrote:

> While Berkeley's critique of 18th century Calculus was right at the 
> time, Abraham Robinson   showed that ultimately that the intuition 
> behind the sort of thing that Leibnitz and others did was right and 
> could be completely formalized and turned into a very powerful tool. It 
> certainly would be nice to implement non-standard analysis in 
> Mathematica (perhaps someone has already done this?). Indeed one can in 
> this way turn calculus into algebra (getting rid of the concept of 
> Limit) and it may well be the most natural approach to calculus via 
> symbolic algebra.
>
> (For more see Abraham Robinson, "Non-standard Analysis", Princeton 
> Landmarks in Mathematics, 1996).
>
>
> Andrzej Kozlowski
>
> Toyama International University
> JAPAN
> http://platon.c.u-tokyo.ac.jp/andrzej/
>
> On Monday, July 29, 2002, at 04:13  PM, John Doty wrote:
>
>> In article <ai06os$1f6$1 at smc.vnet.net>, "Andrzej Kozlowski"
>> <andrzej at tuins.ac.jp> wrote:
>>
>>> Actually on second thoughts I began to suspect that this question is
>>> related to another one posted by Heather, concerning simplifying
>>> expressions in which x is "much larger than" y. I am not at all sure 
>>> if
>>> a sensible calculus of this kind can be developed but obviously 
>>> Simplify
>>>  will not do this.
>>
>> It seems to me that this is essentially a (capital-C) "Calculus" 
>> problem,
>> and unless a simple /.y->0 is what's wanted, the correct tool is 
>> Limit[].
>> Berkeley's critique of 18th century Calculus applies here: while it was
>> essentially antiscientific, his reasoning was flawless and should warn 
>> us
>> against trying to solve this sort of problem by mindless algebra.
>>
>> Of course, Limit[] is a tricky and somewhat unreliable power tool,
>> requiring caution. This reflects the mathematical subtlety of this kind
>> of problem. It is generally essential to formulate the problem in 
>> such a
>> way that the direction of the approach to the limit is unambiguous.
>>
>> --
>> | John Doty		"You can't confuse me, that's my job."
>> | Home: jpd at w-d.org
>> | Work: jpd at space.mit.edu
>>
>>
>>
>
>
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/