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^^ why prove something, when you can just write a program in c to do it for you

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Originally posted by Resnick ^^ why prove something, when you can just write a program in c to do it for you

Amazing! A program that solves for ALL the integers? I want it!

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Originally posted by DigiNut code: #include void main() { int a, b; scanf("%d %d", &a, &b); printf("%d", (a-1)*(b-1) - 1); return; }

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that will fail as soon as a or b are >2^32 on x86 or 2^64 on 64 bit machines.. or 2^128 on 128 bit machines.. well you get my idea, there are integers much bigger than 2^n for n in [0,infinity)

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Originally posted by drizzt81 \ that will fail as soon as a or b are >2^32 on x86 or 2^64 on 64 bit machines.. or 2^128 on 128 bit machines.. well you get my idea, there are integers much bigger than 2^n for n in [0,infinity)

Oh bloody hell, I didn't realize we were getting technical here.

Fine, just set up two linked lists to perform the multiplication, then it will only fail when it runs out of memory. Sure, that's not infinite, but I'd be willing to bet that you'd spend the rest of your life typing in a set of numbers that would cause it to run out of memory.

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Originally posted by DigiNut Oh bloody hell, I didn't realize we were getting technical here. Fine, just set up two linked lists to perform the multiplication, then it will only fail when it runs out of memory. Sure, that's not infinite, but I'd be willing to bet that you'd spend the rest of your life typing in a set of numbers that would cause it to run out of memory.

Hmm... somehow I think he's just trying to point out that any machine must fail when trying to validate an infinite number of inputs. Then again, computers are currently crucial in solving the four-color theorem, so I wont bash them too much.

It also brings up an interesting point from cognitive science about why humans can seemingly use reasoning that seems to be outside of the bounds of Turing machines...

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Originally posted by Flyboy217 Then again, computers are currently crucial in solving the four-color theorem, so I wont bash them too much.

I know we've gotten off-topic, but what is that?

Damn, I feel dumb now! Whatcha guys talkin about again? Guess the answer to this thread would be NO!!!!!!!!!

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Originally posted by DigiNut I know we've gotten off-topic, but what is that?

Draw a 2-dimensional map (like countries for example). You need to color them in such a way that no two bordering countries have the same color (to avoid confusing the map viewers!). Is there a bound for the number of colors you must use to do this?

The answer is 4 (?!). That's right, using 4 colors, you can color ANY map so that no two bordering countries have the same color. It was only eventually proven by enumerating equivalence classes by a computer. Nobody's solved it by hand. I think it's the most famous example of a (partially) computer-proven problem.

I guess the rest shall remain forever unsolved :-D

This is quite easy to show on paper really ...

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Originally posted by Flyboy217 I guess the rest shall remain forever unsolved :-D

Well, only 3(b) and 4(b) are unsolved... I just don't have that much time to work on them lately, I'll get to 'em eventually...

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Originally posted by UWM This is quite easy to show on paper really ...

The four-color theorem? Well props to you if you can, but mathematicians have tried (and failed) for decades.

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Originally posted by Flyboy217 The four-color theorem? Well props to you if you can, but mathematicians have tried (and failed) for decades.

Is this any map you could possibly devise, or just our world map?

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Originally posted by Flyboy217 Draw a 2-dimensional map (like countries for example). You need to color them in such a way that no two bordering countries have the same color (to avoid confusing the map viewers!). Is there a bound for the number of colors you must use to do this? The answer is 4 (?!). That's right, using 4 colors, you can color ANY map so that no two bordering countries have the same color. It was only eventually proven by enumerating equivalence classes by a computer. Nobody's solved it by hand. I think it's the most famous example of a (partially) computer-proven problem.

What about a country with 4 other countries bordering it?

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Originally posted by Flyboy217 The four-color theorem? Well props to you if you can, but mathematicians have tried (and failed) for decades.

Well I don't know if I've necessarily proven it, but I was just toying around with it and came up with what looked to be a solution.

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Originally posted by UWM Well I don't know if I've necessarily proven it, but I was just toying around with it and came up with what looked to be a solution.

i'm piqued. Post a pic and lets see how you did it

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Originally posted by DJ-Fuq What about a country with 4 other countries bordering it?

The center country is colored A and the rest are all B. That's two colors :-)

Yes, this is of course for any possible 2D map, not just our world :-P. That would be a horrible, horrible mathematical theorem.

Four Color Theorem

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