More than Infinity???

[Beaker]

Just a quick thought experiment i thought I would share with you:

There is an infinite number of rooms in a hotel, with an infinite number of guests.
A guest comes to the reception and asks for a room.
What does the receptionist say?

BTW: My favourite answer was: Yeah, sure, last one on the right. :lol:

[huginnmuninn]

the infinite number of guests would breathe up the finite amount of air killing everybody leaving plenty of open rooms

[Electra Heart]

I'm bored so... Let's look at this logically

Well, let's say an average hotel room is 225 square feet, and 10 feet high. From a logical viewpoint, let's give everyone on Earth a room. There are around 6,840,507,003 people on this Earth. So let's do the math, in terms of the amount of volume a hotel would need to accommodate the amount of people on Earth would be 225 square feet x 10 ft = 2250 feet cubed in volume, times the population: 2250 feet cubed x 6,840,507,003 people = 15,391,140,756,750 cubic feet of space. Alright, let's try this with miles, 15,391,140,756,750 / 5280 ≈ 2,914,988,780 cubic MILES of space, only including the rooms in this said hotel, for the amount of people on Earth today. Switching to kilometers here, the estimated volume of the Earth itself is 1.332×109 km3. Said hotel would again, have to be AT LEAST 2,914,988,780 cubic miles OR 4,691,219,703.160 km. So let's see, volume of the Earth=1.322x109km cubed, volume of said hotel≈4,691,219,703. In short, on a scientific level that is impossible.

P.S. I really have NO idea what this is... I just drank spiked Kool-Aid, and pretended I had smarts :)

Funny though :P

[Mortal Coil]

It's infinite. As in, limitless... so the receptionist would probably toss the guy a key with seventeen figures on it and go back to texting her boyfriend in room 758042.. :P

[Sonic Boom]

So there are infinite number of rooms. But these are all occupied by an infinite number of guests! Therefore, the receptionist would have to tell the guy to fuck off and find another place (politely).

[Ryhanna]

Well, if there's infinite rooms and infinite guests and the receptionist walks in then Psyduck.

[Azunite]

There will still be room for another guest.

[Erasmus]

There will still be room for another guest.

^that^

[Thunduhbuhlt]

Infinity is a never ending thing, so I would have to say no, there is not.

[Continuum]

There would be room, of course. However, he would die of exhaustion (And also possibly from CO2 poisoning, since an infinite number of guests would inevitably breathe out an infinite amount of Carbon Dioxide. :lol3:) before he could even reach the room designated to him.

[Peace God]

∞ =/= ∞, its not a defined number. basically, all you're saying is that there's a large unknown quantity of rooms and a large unknown quantity of guests. so the receptionist would probably say that she doesnt know and she's tired of working for a hotel that doesnt keep a record of it's rooms and guests.

[Jess]

∞ =/= ∞, its not a defined number. basically, all you're saying is that there's a large unknown quantity of rooms and a large unknown quantity of guests. so the receptionist would probably say that she doesnt know and she's tired of working for a hotel that doesnt keep a record of it's rooms and guests.

this. ∞ is not a number, it's an idea... like 0 x ∞ is not 0.

[GoofyGal13]

Ohhh, I know this one! What you do is have everyone move down one room. that leaves the first room open for the new guest!

[sammy1996]

Ohhh, I know this one! What you do is have everyone move down one room. that leaves the first room open for the new guest!

This

[Sudds3]

Well....first off that is impossible! So nothing would happen because it can't possibly exist!

But hypothetically, infinity.....goes on forever! The hotel goes on forever and the people do too! So it's in fathomable and improbable. They would give them a room and the endless amount of rooms would continue to be endless same with the people.....it's endless, never ending. Everyone would have a room, even if the people are endless too infinity=infinity simple, and there is no infinity plus 1 because that 1 would just be in line with the endless amount of people. Simple

[Midland]

So there are infinite number of rooms. But these are all occupied by an infinite number of guests! Therefore, the receptionist would have to tell the guy to fuck off and find another place (politely).

I agree with Teejay. For arguments sake lets say both infinities are equal and increase towards infinity in an infinite amount of time (counting/creating each room/person takes a small amount of time). That then means that as a new room was created it would be instantly filled providing no room for the new comer.

[Anselmo]

Some infinities are bigger than others, so assuming that there are more guests than rooms that guy will probabily spend the night somewhere else.

[Sudds3]

I don't think so....infinity means that it has no limit basically. But if you mean infinity refers to a number greater than any real number than any real number then yes. But I think that the big man23 is thinking of infinity as going on forever, not as any single Unreal number greater than any real number. So he is asking what would happen if you had an amount rooms that went on forever and an amount of people that went on forever in those rooms...then another man walks up and asks for a room. Then what would happen.

[Peace God]

I don't think so....infinity means that it has no limit basically. But if you mean infinity refers to a number greater than any real number than any real number then yes. But I think that the big man23 is thinking of infinity as going on forever, not as any single Unreal number greater than any real number. So he is asking what would happen if you had an amount rooms that went on forever and an amount of people that went on forever in those rooms...then another man walks up and asks for a room. Then what would happen.
uhh... same thing. you're just wording the same concept in different way.
there's no practical difference between something that goes on "forever" and something that goes on for a large undefined amount of something.

[Sudds3]

uhh... same thing. you're just wording the same concept in different way.
there's no practical difference between something that goes on "forever" and something that goes on for a large undefined amount of something.

Oh.....hahaha sorry! I'm really not that smart and I just think I am! Hahahahahahahahahaha, wow I look STUPID! It made sense in my mind, well I usually over think things and make things so much more complex than they need to be. Oh well

[Korashk]

I'm bored so... Let's look at this logically

Well, let's say an average hotel room is 225 square feet, and 10 feet high. From a logical viewpoint, let's give everyone on Earth a room. There are around 6,840,507,003 people on this Earth. So let's do the math, in terms of the amount of volume a hotel would need to accommodate the amount of people on Earth would be 225 square feet x 10 ft = 2250 feet cubed in volume, times the population: 2250 feet cubed x 6,840,507,003 people = 15,391,140,756,750 cubic feet of space. Alright, let's try this with miles, 15,391,140,756,750 / 5280 ≈ 2,914,988,780 cubic MILES of space, only including the rooms in this said hotel, for the amount of people on Earth today. Switching to kilometers here, the estimated volume of the Earth itself is 1.332×109 km3. Said hotel would again, have to be AT LEAST 2,914,988,780 cubic miles OR 4,691,219,703.160 km. So let's see, volume of the Earth=1.322x109km cubed, volume of said hotel≈4,691,219,703. In short, on a scientific level that is impossible.

P.S. I really have NO idea what this is... I just drank spiked Kool-Aid, and pretended I had smarts :)

Funny though :P
Your math strikes my gut as being wrong in some way, or you're just misinterpreting what your values mean. People take up such a tiny amount of the actual space on Earth that I doubt making a single hotel room for everyone would require all the space that there is and then some. The calculations alone require calculus to even attempt.

It's much easier to calculate using surface area as your base, because we can go up all day to get to that volume.

225ft^2*7 Billion = 1,575,000,000,000ft^2
That/5280ft/mile = 298,295,455miles^2
Convert to km = 480,060,001km^2

That's enough floorspace for the 7 billion rooms if I did my math right. The surface area of Earth is 510,072,000km^2. So, there'd be enough room. Heck, the initial value even assumes that this is a one story hotel. Increase the floors and that initial value goes WAY down.

[Incompris]

If there was an infinite number of rooms then there would be one for that person. Be a pain to find but hey there would still be one.

[Aves]

It's simple, we blow up the hotel.

[Mordecai]

Wouldn't more than infinity just defeat the concept of infinity?

Something else to contemplate would be if infinity even exists.

[double r]

Just a quick thought experiment i thought I would share with you:

There is an infinite number of rooms in a hotel, with an infinite number of guests.
A guest comes to the reception and asks for a room.
What does the receptionist say?

BTW: My favourite answer was: Yeah, sure, last one on the right. :lol:

Good luck finding the dam room. We are not liable, for any causes during finding the room, or getting lost in the hall/ wilderness. Your room is going to the 2000000000000000000^2 on the right.
Thank and enjoy you stay.

Thats what the receptionist said to me.

[Noirtier]

The receptionist would say "Welcome! Let me check our database to see our free rooms." She would look on the hotel's computer database which would then overload at the infinite number of rooms and guests in the hotel, and the system would crash. The receptionist then looks at the guest and says, "Screw it. Here's a key go figure out what it's to."

[Bharris13]

I've seen this very problem on a tv show (yes I'm sad) and it is quite simple. If there is an infinite amount of people in an infinite amount of rooms then you ask every person to move 1 room up (E.g. person in room 1 to go into room 2, room 2 into room 3 etc.) and room 1 will end up free. This can happen with any amount of people entering the hotel as there is an infinite amount of rooms.

[Desuetude]

Turn on the fire alarm and make everyone go outside, the man that wanted a room is likely to bag one of the unattended ones seeing as it'd be pretty impossible to find your way back and most of the people would die in corridors or something.

[kenoloor]

Infinity (http://en.wikipedia.org/wiki/Infinity) is a concept not a number. The very concept of infinity represents something without limits. Therefore, your scenario is impossible/irrelevant.

/thread

[Bharris13]

Infinity (http://en.wikipedia.org/wiki/Infinity) is a concept not a number. The very concept of infinity represents something without limits. Therefore, your scenario is impossible/irrelevant.

/thread
In mathematics, infinity has been made a number. They did this in order to piece together various equations that required infinity. Exactly how they did this I don't know (I think there is a program on youtube about it). Obviously, the scenario is impossible, it is hypothetical and the infinite hotel problem is used to explain the properties of infinity and how infinity minus infinity can equal any possible number.