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 > > >