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MathGroup Archive 2003

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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
>
>
>



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