School Help - Infinity

[Afrobean]

Re: School Help - Infinity

infinite amount

Please... don't say this. Infinite is not a quantity. If it was a quantity, it would simply be a very large number (possibly an infinitely large one? haha), and as such would not actually be infinite.

Actually, I think this is the underlying problem with this in my mind. Infinite is not a quantity, and as such, you cannot "fill" a hotel with capacity of infinite, even if it were possible to have an "infinite amount" of guests.

One more thing I think someone else already touched on: it would be impossible unless the move were done at a rate of infinite people per 0 seconds. Now, not only does that not make any sense at all, but it is also not only physically impossible, but also logically impossible as far as I can figure.

[Reach]

Re: School Help - Infinity

Please... don't say this. Infinite is not a quantity. If it was a quantity, it would simply be a very large number (possibly an infinitely large one? haha), and as such would not actually be infinite.

Actually, I think this is the underlying problem with this in my mind. Infinite is not a quantity, and as such, you cannot "fill" a hotel with capacity of infinite, even if it were possible to have an "infinite amount" of guests.

One more thing I think someone else already touched on: it would be impossible unless the move were done at a rate of infinite people per 0 seconds. Now, not only does that not make any sense at all, but it is also not only physically impossible, but also logically impossible as far as I can figure.

There's nothing wrong with saying an infinite amount. An amount is how much of something. You have infinite people in the hotel. I am well aware of infinity being a concept.

Really, your problem is that you keep trying to visualize the problem XD You can't afro. As much as you, and I, would like to try and visualize it happening, you can't and it only confuses the hell out of you.

Also, you're right, you're never going to get everyone in unless the rate of movement is infinite. But that doesn't matter - You can keep fitting people in and in a hypothetical sense, can fit everyone in if you want to. Remember, it's hypothetical, stop talking about it like it is a real event.


Oh yea, one more thing.

The thread is going to turning into a squabble fest soon. Can anyone refute my method of getting everyone into the hotel? Noone has even addressed it (probably because it works ;p). There's no point in just going off on a tangent about your opinion here; the man asked a question and wanted an answer (which he now has, unless there are alternative answers to the problem at hand, not your own hypothetical problem ;p).

[Tokzic]

Re: School Help - Infinity

Actually, I think this is the underlying problem with this in my mind. Infinite is not a quantity, and as such, you cannot "fill" a hotel with capacity of infinite, even if it were possible to have an "infinite amount" of guests.

This is true - I ignored it to follow through on the problem as much as I could, but again, we have ∞/∞ as the equation for number of people per room in the old town.

If you ask me there are so many logic crossroads that this question is hardly worth answering. He's probably just seeing what thought processes everyone goes through and throws them marks if they look at all well-thought out.

Reach, you don't even verify that you could fit that many people in the new hotel. Establish that how you can before you even touch on the "if so, ..."

[CMAxX400]

Re: School Help - Infinity

TECHNICALLY, infinity is a concept of running on forever with no end (was that redundant?). But, if you take infinity and turn it into a ridiculously large number, as Afrobean said, it will destroy the concept of infinity as a whole. Besides, if cannibals (I agree your math teacher is weird...) came and tried to destroy the hotels, they have a problem: All of the hotels can never be destroyed.
Honestly, I think that this is some kind of trick question involving an infinity paradox...but don't take my word for it. I'm not in Precalculus yet.

[Reach]

Re: School Help - Infinity

Reach, you don't even verify that you could fit that many people in the new hotel. Establish that how you can before you even touch on the "if so, ..."

You already agree ∞+∞=∞. It comes down to more specficially, how you place the infinities into the hotel. This has nothing to do with the hotel being able to hold that many people or not, because the hotel has an unlimited number of rooms.

It is a paradox. Which is probably why so many people are confused. Here's how it would go (you are the manager 8) )

Tok: Yo, wats up?
dude: yo I got infinity men right here that need a room. Iz u hotel full?
Tok: We're full yo
dude: Wat? We can't get in?
Tok: Oh, yes we have room for your men
dude: wat???
Tok: We have rooms ready for you
dude: yo u said u was full
Tok: We are
dude: you ain't makin no sense
Tok: I know

Ad nauseum. It's a fun scenario ^^

But this is so fruitless...

Put it this way, if you can't count the infinities (i.e. you can't put them into groups of infinite sets) then you, for all practical purposes would win because we wouldn't be able to fit everyone in because of what I've already said before. However, as long as you can count the infinities then you can place the counted infinities into the hotel properly with the correct method.

If it's any consolation for it all, a similar question puzzled philosophers and mathematicians for a very long time. I think Galileo had it figured out.

All of the hotels can never be destroyed.

They can, and I already said how.

Don't turn this into the other infinity thread we have going...or did it die yet finally?

[inflames07]

Re: School Help - Infinity

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.

[Reach]

Re: School Help - Infinity

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

[inflames07]

Re: School Help - Infinity

I just don't see how you could work with the number infinity, that's all.

[Tyren]

Re: School Help - Infinity

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.

[EternalWrath]

Re: School Help - Infinity

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.

[Tyren]

Re: School Help - Infinity

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.

[devonin]

Re: School Help - Infinity

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.