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



Maybe there are better examples, but try this:

 (%i7) trace(?simplus,?simptimes);
 (%i8) limit(((sqrt(x+1)-sqrt(x)))*cos(x),x,inf);
  < junk deleted>
 
You'll discover that Maxima does extended real arithmetic about three times.
Each time, it is done incorrectly. After three spurious internal calculations,
Maxima says the limit is undefined. The correct value is 0.

Also, the way the limit function uses 1.0e-8 and 1.0e8 internally is embarrassing.
Sorry to be so grumpy today. 

--Barton