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Suuuuuuuuuure. https://forums.windrivers.com/images.../2005/03/1.gifQuote:
Originally Posted by Cobra X
Welcome aboard anyhow.
Don't worry, this doesn't mean you have to wear the WOTPP thong now. https://forums.windrivers.com/images.../2006/04/1.gif
Suppose that, somewhere in New Jersey, there is a hotel with an infinite number of rooms.
You arrive late one night and ask the front desk clerk if they have a vacancy. He replies that every room is occupied, however, he can arrange for you to get one. But how, you wonder, if there is no vacancy? The answer is simple: the clerk will simply ask the people in room 1 to move to room 2, those in room 2 to move to room 3, those in 3 to move to room 4, and so on. Since there is an infinite number of rooms, everyone will have a room to move into, and room 1 will be available for you.
Hotel Infinity is an amazing place, you think to yourself as you sign in. But just as the clerk is about to give you your key, an infinite number of people arrive for an APA convention. The clerk cleverly figured out how to get you a room, but can he accommodate an additional infinity of guests?
__________
Amazingly, he can. He just asks everyone to move again, but this time to the room number that is twice the number of their current room. In other words, you would move to room 2, the people in 2 would move to 4, those in 3 to 6, those in 4 to 8, and so on. This will leave all odd numbered rooms — an infinite number of them — vacant.
This paradox illustrates an unusual property of infinite sets. With finite sets, a (proper) subset will always contain fewer members than the entire set. A part is smaller than the whole. But with infinite sets that is not the case: one part of the set can be just as large as the whole. For example, there are as many even numbers as there are natural numbers, even though the natural numbers contain all the even numbers plus the odd ones as well. This can be seen by pairing the natural numbers with the even numbers to show that there is a one-to-one correspondence between the two sets:
1 2 3 4 5 6 ...
| | | | | |
2 4 6 8 10 12 ...
Likewise, even though only some numbers are perfect squares (1, 4, 9, 16, 25, ...), and the distance between each perfect square becomes greater and greater as we progress down the number line, there are as many perfect squares as there are natural numbers. For each natural number is the square root of exactly one perfect square. (This is sometimes known as Galileo's Paradox, as it was first pointed out by the famous Italian physicist and astronomer.)
A variation on hotel infinity results in an interesting Zeno-style paradox. Contrary to what might first be supposed, the hotel doesn't have to occupy an infinite space. Suppose the hotel has one room per story. If each room is half the height of the one below, then the entire structure will be only as tall as a two-story building. But if that's the case, then it should have a roof on top. And if it has a roof, then, as any reputable architect can point out, the other side of it ought to be the ceiling over some room. However, what room will that be, given that the hotel has an infinite number of them and therefore no top story?
Why not just have them go to the rooms that aren't taken yet ? Is there some premise that the guests have to start in room 1 ?Quote:
Originally Posted by a d e p t
Alternatively, the actual answer to the question is yes.Quote:
Originally Posted by a d e p t
Now THAT is a cheap way of getting a point and preventing someone else from claiming 3 for themselves! :pQuote:
Originally Posted by edball
Why, Thank You. https://forums.windrivers.com/images.../2005/03/1.gifQuote:
Originally Posted by a d e p t
Quote:
Originally Posted by edball
Very sneaky.
Deity would disapprove, I'm sure. :D
Who ? I thought you deleted inactive players. https://forums.windrivers.com/images.../2005/03/1.gifQuote:
Originally Posted by a d e p t
Yes. He can simply request that each guest move to the room twice its number minus one (the people in room 2 move to room 3, 3 to 5, 4 to 7, 5 to 11 etc.). This will leave all the even numbered rooms open. The set of all even numbers is also infinite even thought it seems it should be half of the set of whole numbers.Quote:
Originally Posted by a d e p t
Actually, I thought too hard. They can just move to each room x2 and leave all the odd rooms open.
Quote:
Originally Posted by Mindwarp
I was 100% sure no one would get this one! https://forums.windrivers.com/images.../2005/03/1.gifQuote:
Originally Posted by Mindwarp
I can only give you a single point, since the answer had already been given, but please accept this bonus point as a token of my esteem fot you having memorized the entire Google cache. :p
you could keep moving peoples from room 1 to 2 to 3... for each of the infinite new guests, since there's an infinite numbers of rooms and you will not run out of room.
but moving from rooms take time, so the night have to be infinite to do that, and since they will all keeps moving all night, they won't have time to sleep.
and if they cant sleep with bother with a room?
add the peoples leaving because they cant sleep anyway, the guest who will refuse to moves from their rooms, those who will sue the hotel because of all this
and you end up with CHAOS!!!
but New Jersey can lives with more chaos so yes you can fit them in the hotel
Not yet.Quote:
Originally Posted by edball
I just thought about it real hard.
You can give him my point, it was just a technicality.Quote:
Originally Posted by a d e p t
"Her", unless I'm mistaken. ;)Quote:
Originally Posted by edball
Not only the minions get cool chicks to hang out with them. :D