> > One of the marvels of computing today is that it is possible to do so > much in such a short time. > One can execute billions of instructions a second. If only > one in a million does the wrong thing, and is wrong only > by a tiny percent, you can accumulate a whopping mistake > in a second. >
When I have given introductory Mathematica courses, one of the things I would point out early on, was that you should never implicitly trust Mathematica to get an answer that was important to you.
By that, I did not mean what you seem to mean - that Mathematica was particularly buggy - because it is not, but every substantial piece of software contains some faults, and fingers contain bugs too - so it is easy to mistakenly type something like:
and be be amazed by the answer. Likewise, systems of equations can be numerically unstable and generate junk.
It might almost be better to train students on slightly faulty software to make them more vigilant!