"Stefan Wolfe" wrote in message
...

"Mike Kaliski" wrote in message
...

Integral calculus has been described as one of the greatest advances in
mathematical science, but that is still only an approximation method and
nobody complains about that.

Mike, it is hard for me to let this go (but it is off topic). Integral
calculus is not an approximation, it is exact. The prior art, the
summation method of adding the areas of small rectangles, was the
approximation. The genius of integral calculus was that it was able to sum
an infinite number of infinitely small rectangles and come up with an
exact answer. For the answer to be exact, it was necessary to deal with
infinity (undefined) and the concept actually works. It even works in many
cases where there is an asymptote that is infinitely long (f(x) =
1/x**2)).
END OF COMMENT (no, I will not offer experimental proof that integral
calculus is exact :-))
Stefan

All true and it works very well. It's just that being forced into accepting
such concepts as infinity and the square root of minus one without being
able to pin down exactly what they are shows up how limited we are in our
abilities to deal with the true nature of the universe. How can anyone
really get to grips with such concepts as an infinity of infinities?

Mike G0ULI