Arbitrary precision calculations

[Jim Hefferon]

Perhaps you need to specify a little more what you mean here.  Comparing
two arbitrary precision decimal expansions (this is what I thought you
meant, but maybe I'm mistaken) is not possible, in two senses.  First,
if you just simply want to compare them on a per-decimal place basis
then you will never be able to finish to conclude `equal', you can only
conclude `unequal' (I'll ignore the .999...=1 problem; see the sci.math
FAQ).  Second, if you want to conclude that they have equivalent 
algebraic descriptions (say, decide that 1+\sqrt{2}=\sqrt{2}+1) then 
you are again in hot water because this is an undecidable problem;
IIRC it is equivalent to the Halting Problem.

Jim Hefferon