Re: Epsilon-Delta proofs
- To: mathgroup at smc.vnet.net
- Subject: [mg39553] Re: [mg39540] Epsilon-Delta proofs
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sun, 23 Feb 2003 04:59:48 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Yes, you can certainly do this, although of course you must restrict
yourself to rational functions since the method (due to Adam
Strzebonski) is entirely algebraic:
<< "Experimental`"
<< "Developer`"
Resolve[ForAll[\[Epsilon], \[Epsilon] > 0,
Exists[\[Delta], \[Delta] > 0,
ForAll[x, 2 - \[Delta] < x &&
x < \[Delta] + 2 &&
\[Lambda] \[Element] Reals,
-\[Epsilon] < (x^2 - 4)/
(x - 2) - \[Lambda] < \[Epsilon]]]]]
-4 + \[Lambda] == 0
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/
On Saturday, February 22, 2003, at 05:37 PM, Will Self wrote:
> It occurred to me that it might be interesting to write a Mathematica
> program that would do epsilon-delta proofs for limits, e.g., prove
> that the limit of (x^2-4)/(x-2), as x approaches 2, is 4. Perhaps
> restricting the expressions involved to rational functions. Has
> anybody done something like this?
>
> email replies greatly appreciated
> Will
>
>
>