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