Extended real arithmetic (was Re: inf - inf = 0 ??)



I am a little skeptical about it.  My biggest concern is that the axioms of extended real or complex arithmetic may not 
be self consistent.  If that is the case then you could prove that an answer is correct and incorrect at the same time 
by using different methods perhaps.  If they are in fact self consistent and complete than I am all for it.

Rich



From: Stavros Macrakis
Sent: Friday, September 10, 2010 10:03 AM
To: Barton Willis
Cc: maxima List
Subject: Re: [Maxima] Extended real arithmetic (was Re: inf - inf = 0 ??)


Especially disappointing because extended real arithmetic can in fact solve this correctly:


   p1: sqrt(x+1)-sqrt(x)$
   p2: cos(x)$


limit(p1,x,inf) => 0
limit(p2,x,inf) => IND


from which Maxima should be able using extended real arithmetic that limit(p1*p2) => 0


On Fri, Sep 10, 2010 at 08:52, Barton Willis <willisb at unk.edu> wrote:

  (((sqrt(x+1)-sqrt(x)))*cos(x),x,inf);




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