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Mega X.exe
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Hilbertís Hotel is a hotel with an infinite number of rooms, each one of which is occupied. The hotel gives rise to a paradox: the hotel is full, and yet it has vacancies.

That the hotel is full is obvious. It has an infinite number of rooms, and an infinite of guests; every room is occupied. That the hotel has vacancies is a little more difficult to demonstrate.

Suppose that a new visitor arrives; can he be accommodated? At first it seems that he cannot, but then the hotel clerk has an idea: He moves the guest in Room 1 to Room 2, and the guest in Room 2 to Room 3, and so on. Every guest is moved to the next room along.

For every guest, in every room, there is another room into which they can be moved. This leaves Room 1 vacant for the new visitor. Although the hotel is full, then, the new guest can be accommodated in Room 1.

It is not only one new guest that can be accommodated; in fact, Hilbertís Hotel has an infinite number of vacancies. By moving every guest to the room the number of which is double the number of their current room, all of the even numbered rooms can be vacated for new guests. There are, of course, an infinite number of even numbered rooms, and so an infinite number of new guests can be accommodated.


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Serpentarius
13th Zodiac Sign: Snake
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Hmm...

Well, if there is an infinite number of rooms and they're all full, then you have a conundrum with the definition of infinity. Infinity, as I and possibly a few mathematicians view it, is like that arrow at the "end" of a number line. It can extend on forever, and therefor is not a real number. Trying to add a real number such as 1 to a non-real number such as infinity is impossible; it's like trying to come up with a single number when adding 4+7x. You get a binomial, no matter how hard you try. Therefor, your occupancy would be infinity+X, where "X" is the number of people being added to the hotel.


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Heatman.EXE
The Red Comet
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I think I agree with Serpentarius... *easy way out* :lol:

But also, I believe that the problem of who would stay in the hotel is a situation-stopper itself. If people enter a hotel to rest, but they are moved every time a new member arrives, they never get to rest. The inability of the hotel to provide its customers' needs would lead to a loss of customers. If people stop entering the hotel looking for rooms (which will happen if these are average people looking for average rooms), then their will be no one residing there, and.....

Agh! That didn't make any sense at all... safe to say, this would simply mean the people originally residing there would get a good night's sleep for once... until the hotel needed to be torn down, which is impossible because an infinite number of rooms can not be destroyed... unless they collapsed it, in which case ALL (extending to infinity) of the hotel would fall, right?


Ouch... X_X


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Originally posted by Breakman:
Saturdays: The day Protoman comes over. He doesn't do or need anything, but Roll insists Rock to sit down and talk to him. So commences the 12-hour awkward silence treatment until Protoman disappears when everybody's back is turned.

God
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Uh... I don't think that meant anything Heatman >.>.

God
Not A Feminist
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Uh... I don't think that meant anything Heatman >.>.