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#21 | |
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FFR Player
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I see "destroying" as subtracting. Infinity is undefined, so if you try to subtract from infinity, you still get undefined. Which means no matter how much you destroy, there will still be infinite amount of hotels.
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#22 |
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FFR Simfile Author
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It's not undefined. More specifically it is 'indeterminate', meaning you don't know without using some calculus. That's because it depends on the size of the infinities you're dealing with. It is possible infinity-infinity could equal zero.
I don't know why you're so hung up on something that has nothing really to do with the question anyway ;p
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Last edited by Reach; 03-31-2007 at 10:56 AM.. |
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#23 | |
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FFR Player
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I just don't see how you could work with the number infinity, that's all.
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#24 |
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FFR Player
Join Date: May 2004
Posts: 40
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Wrath, If I were you I would only spend a short time talking about the logical factors of organizing two infinitely large hotels into one infinitely large hotel. Enough people in here have given you information on that subject. More importantly I would attempt to deduce your Teacher's thought process on making the question itself. It was mentioned once before, but because of how irrelevant the literal question is, he is likely testing your approach to the situation more then anything else. Just be very logical in your assertions, and play into what your teacher is looking for.
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#25 |
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FFR Player
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First of all, we already determined that my math teacher was weird. Even if you could destroy an infinite amount of hotels... we're dealing with cannibals, so it's not a realistic situation on mulitple levels.
The prime number strategy (a la Reach's strategy) seems to be the best, the only problem being that it leaves a lot of empty hotel rooms being unused. Who goes in room 666? The Devil, bad example... how about room 24? It is not a prime number, and not the product of a prime number to a certain power. Aside from those empty rooms that nobody would go into, it would work, but my teacher said that there was a way to do this "that didn't leave so many rooms unoccupied," and I think he was referring to this approach.
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#26 |
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FFR Player
Join Date: May 2004
Posts: 40
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I dont believe I was thinking about this question hard enough when I gave my opinion. Wrath you mentioned that youve yet to look at modulo, so im guessing you havent thought about hashing the two hotels? Im pretty shakey when it comes down to the syntax used but you could set an infinite amount of arrays where each one is a section of the hotel, say every 10 rooms. When you modulo the room number by the the length of the array, the remainder will lie in between the bounds of the array, which will be used as the index for placement. Since you've got two hotels to organize, youll have some collisions. I think this problem can be solved by assigning people from each hotel to n-1 and n arrays respectively.
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#27 |
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Very Grave Indeed
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Your test question is a thought experiment called "Hilbert's Hotel" after the 19th century mathemetician who came up with it. It's actually fairly easy to do once you know how to spell it out.
The hotel has an infinite number of rooms, numbered 1, 2, 3, 4, 5...and on indefinately, and when you arrive, the hotel has infinitely many guests and is thus full. However, if they simply move the person from room 1 into room 2, and room 2 into room 3, with the person in room N going into room N+1 room 1 is now vacant, and you can move into it. The hotel is now full. But then, disaster, a bus shows up with infinitely many passengers and they all want to check in as well. You solve it in much the same way, but instead of just moving everyone up "infinity" rooms which makes little logistical sense, you just move everyone into the even numbered rooms, 1 into 2, 2 into 4, 3 into 6, 4 into 8 and so on up the line, at which point every odd numbered room (of which there are an infinite number) are now vacant, and you move all infinity of them into the infinitely large number of odd-numbered rooms. Room for everyone again. |
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