On 20/11/2021 22:59, Avi Gross via Python-list wrote:
there are grey lines along the way where some
mathematical proofs do weird things like IGNORE parts of a calculation by
suggesting they are going to zero much faster than other parts and then wave
a mathematical wand about what happens when they approach a limit like zero
and voila, we just "proved" that the derivative of X**2 is 2*X or the more
general derivative of A*(X**N) is N*A*(X**(N-1)) and then extend that to N
being negative or fractional or a transcendental number and beyond.
You seem to be maligning mathematicians.
What you say was true in the time of Newton, Leibniz and Bishop
Berkeley, but analysis was made completely rigorous by the efforts of
Weierstrass and others. There are no "grey lines". Proofs do not
"suggest", they PROVE (else they are not proofs, they are plain wrong).
It is not the fault of mathematicians (or mathematics) if some people
produce sloppy hand-wavy "proofs" as justification for their conclusions.
I am absolutely sure you know all this, but your post does not read
as if you do. And it could give a mistaken impression to a
non-mathematician. I think we have had enough denigration of experts.
Best
Rob Cliffe
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