[Haskell-cafe] is proof by testing possible?
muad
muad.dib.space at gmail.com
Mon Nov 9 17:22:00 EST 2009
I have come across an example:
> However, the following proof of the lovely identity:
> sum . map (^3) $ [1..n] = (sum $ [1..n])^2 is perfectly rigorous.
>
> Proof: True for n = 0, 1, 2, 3, 4 (check!), hence true for all n. QED.
>
> In order to turn this into a full-ﬂedged proof, all you have to do is
> mumble the following incantation:
> Both sides are polynomials of degree ≤ 4, hence it is enough to check the
> identity at ﬁve distinct
> values.
>
from http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/enquiry.pdf
Now this sort of idea surely applies to more than just number theory?
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