> Yes, it does mean that. limit(expr1,x,a)-limit(expr2,x,a)
> is not always equal to limit(expr1-expr2,x,a);
>
> An example
> limit(1/x^2,x,0)-limit(1/x^4,x,0);
> inf - inf /* which Maxima converts to 0 */
>
> limit(1/x^2-1/x^4,x,0);
> minf
This is precisely why, I think, the current behavior is not really good. I
don't know if there is a CAS equivalent of the part of the Hippocratic Oath
that is about doing no harm to patients, but if there isn't one, let me
propose it: whatever we do, first and foremost we shall never produce
incorrect results. The expression, limit(1/x^2,x,0) - limit(1/x^4,x,0), is
no more equal to zero than 2x2 = 5. If a CAS evaluates it to zero, that is
an incorrect result. People who trust that CAS and use it to evaluate
complicated expressions (in which such sums may occur and get simplified
without ever being seen by the user) will be misled. Not producing a desired
simplification can be annoying, but not nearly so annoying as producing the
wrong simplification.
Viktor