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Does infinity exist?

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Re: Does infinity exist?

#11

Post by damoncali »

recursive wrote: post #7
ajanuary wrote: post #6

Earlier quoted context omitted.

I'm gunna have to be one of those people that says "really? O_o" when presumably everyone else clearly grasps the concept. I get that if you had an infinite number of rooms, and an infinite number of guests staying, you still have room for an infinite number more guests. But in your example, surely "occupied" is, more than just an indicator of another guest, a state of the room. You have an infinite number of occupie…

The classic approach is to move all the existing guests from room n to n+1 and put the new party in room 1.

Aren't there already guests in room n+1?

Re: Does infinity exist?

#12

Post by taejo »

inportb wrote: post #10
Swizec wrote: post #3

My favourite example of infinity is this: "You own a hotel with an infinite number of rooms, all of which are currently occupied. A group of four guests comes and wants to rent a room. Do you have a room for them?" The answer is that yes, you do in fact have room for infinitely more guests.

a hotel with an infinite number of rooms, all of which are currently occupied So you have an infinite number of occupied rooms. That is, you have a one-to-one mapping between rooms and parties. Do you have room for more guests? I don't think so, because none of the rooms are unoccupied. You could try to free up some space by consolidating parties, though.

You don't have to consolidate, just move people: move the occupants of room n to room 2n and now you have infinitely many empty rooms (all the odd-numbered ones).

Re: Does infinity exist?

#14

Post by [deleted] »

recursive wrote: post #7
ajanuary wrote: post #6

Earlier quoted context omitted.

I'm gunna have to be one of those people that says "really? O_o" when presumably everyone else clearly grasps the concept. I get that if you had an infinite number of rooms, and an infinite number of guests staying, you still have room for an infinite number more guests. But in your example, surely "occupied" is, more than just an indicator of another guest, a state of the room. You have an infinite number of occupie…

The classic approach is to move all the existing guests from room n to n+1 and put the new party in room 1.

[deleted]

Re: Does infinity exist?

#15

Post by davmre »

drblast wrote: post #5

My favorite thought experiment that I think is relevant here is to try to pick a truly random number. If you think about it, this is impossible, because the act of picking a number limits you to a finite set of numbers that you have considered. Put another way, you can't pick numbers from an infinite sample space because you can't create an infinite sample space. This has all sorts of odd implications, like the two e…

Put another way, you can't pick numbers from an infinite sample space because you can't create an infinite sample space.

That's not true; there's nothing wrong with infinite sample spaces. It's just that there's just no such thing as a uniform distribution over an infinite space.

For example, suppose you flip a fair coin repeatedly until the first time it comes up Heads. The number of flips you end up making could be any positive integer, so this procedure samples from an infinite space. But not all integers are equally likely. (in fact, each integer is half as likely as the one before, following a geometric distribution).

Re: Does infinity exist?

#16

Post by inportb »

taejo wrote: post #12
inportb wrote: post #10

Earlier quoted context omitted.

a hotel with an infinite number of rooms, all of which are currently occupied So you have an infinite number of occupied rooms. That is, you have a one-to-one mapping between rooms and parties. Do you have room for more guests? I don't think so, because none of the rooms are unoccupied. You could try to free up some space by consolidating parties, though.

You don't have to consolidate, just move people: move the occupants of room n to room 2 n and now you have infinitely many empty rooms (all the odd-numbered ones).

... which would consolidate the occupants of rooms n and 2n (and there are people in room 2n to begin with, if all of the rooms are indeed currently occupied).

edit: I see that the folks in 2n would now be in 4n, and so on down the chain. You'd always have some guests that are in the process of being evicted (i.e. between rooms); then again, that's negligible because we're not talking about real life (™). Clever!

Re: Does infinity exist?

#17

Post by damoncali »

Cushman wrote: post #13
damoncali wrote: post #11

Earlier quoted context omitted.

Aren't there already guests in room n+1?

No, those guests now stay in room n+2.

I don't get it. Can't I just as easily say that n+2 is also occupied? After all, they're all occupied by definition, aren't they?

For example. All blocks are either red or blue. You have an infinite number of blocks that are all red. Do you have any blue blocks? No. Where is the mistake in my logic?

Re: Does infinity exist?

#20

Post by bmm6o »

drblast wrote: post #5

My favorite thought experiment that I think is relevant here is to try to pick a truly random number. If you think about it, this is impossible, because the act of picking a number limits you to a finite set of numbers that you have considered. Put another way, you can't pick numbers from an infinite sample space because you can't create an infinite sample space. This has all sorts of odd implications, like the two e…

Well, the real problem is that there is no uniform distribution on the integers.
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