email@example.com (Dr D F Holt) wrote: (...) >whole number calculations. (As far as I know, the proof of the four color >theorem does not involve any real number arithmetic - correct me somebody >if I am wrong.)
I've not said that the proof of this theorem involved any floating point arithmetic. Neither that I disagreed with the fact that it's proved. I only stated that there are people who doesn't accept.
>As I said in an earlier post, the only meaningful question that you can ask >about a proof is how likely is it that it is correct, and that is independent >of the method used.
What's a proof? I think it's a sequence of symbols. What's the process of verifying a proof? To see if that sequence is "valid" given some rules. If the method you used gives me a correct finite sequence of symbols, that's what we expected. But since it has finiteness, it has the property that it can be worked out with paper and pencil only.
>Do you believe that 7^sqrt(8) > 8^sqrt(7)? If so, why? >A couple of very nice methods of proving this using only arithmetic that >can be done on paper and pencil have been posted, but despite that, I >personally still find the straightforward calculator "proof" the most >convincing, and the most likely to be free of error.
I think this is turning out to be a flame war from your part; anyway, let's continue: if I don't have a justification to the method, I can't accept something. And saying: "my calculator `said' this" isn't a strong justification. If you can show me why you've accepted every step in the proof done with your proof using your calculator, then there's no problem with the proof (but I think this will be longer than the answer asked by the original poster for example). But if you can't, well, that is a wrong answer as wrong as saying that 0 = 1 (when we are dealing with real numbers, let me state this before someone get some weird algebraic structure :) ).
-- ====================================================================== Rogerio Brito - Computer Science Student - University of Sao Paulo e-mail: firstname.lastname@example.org - home page: http://www.ime.usp.br/~rbrito "Windows? Linux and X!" - Member of Linux Users Group in Brazil ======================================================================