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Topic: 7^sqrt(8) > 8^sqrt(7) proof
Replies: 2   Last Post: Jun 15, 1996 5:22 AM

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Rogerio Brito

Posts: 122
Registered: 12/12/04
Re: 7^sqrt(8) > 8^sqrt(7) proof
Posted: Jun 13, 1996 4:21 PM
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mareg@csv.warwick.ac.uk (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 :) ).

[]z, Roger...

--
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Rogerio Brito - Computer Science Student - University of Sao Paulo
e-mail: rbrito@ime.usp.br - home page: http://www.ime.usp.br/~rbrito
"Windows? Linux and X!" - Member of Linux Users Group in Brazil
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