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MathGroup Archive 2002

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Re: Question about Replace

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35753] Re: Question about Replace
  • From: "John Doty" <jpd at w-d.org>
  • Date: Mon, 29 Jul 2002 03:13:27 -0400 (EDT)
  • References: <ai06os$1f6$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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


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