A (maybe noob) question: Let
a = 1234567891234567889998.5 b = 1234567891234567889999.5
Mathematica (v8) yields for
a*0.5 - b*0.5
0. (wrong answer) and
(a - b)*0.5
-0.5 (correct answer)
although both expressions
a*0.5 - b*0.5 and
(a - b)*0.5 are mathematically identical. I set
$MinPrecision = 200, to no avail.
Is there a way to get for both analytically identical expressions the same numerical result? In my original mathematical problem I want to compare two representations of the same problem, with one yielding a vast sum over products of binomial coefficients (yielding numerically results of order
n > 10) with tiny numbers (order
0.1^2^n). Analytically I cannot simplify the expressions.
Thanks a bunch.