Does infinity exist?
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Does infinity exist?
1–10 of 127 posts
Re: Does infinity exist?
#2If this interests you, I can recommend David foster Wallace's "Everything and more"
Re: Does infinity exist?
#3My 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.
Re: Does infinity exist?
#4My 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.
I'm assuming that you have a hotel with a countably infinite number of rooms all of which are occupied. In that case you have room to accommodate a finite or countably infinite number of new arrivals.
Re: Does infinity exist?
#5My 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 envelope paradox: http://en.wikipedia.org/wiki/Two_envelopes_problem
Enjoy!
Re: Does infinity exist?
#6My 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.
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 occupied rooms, but zero unoccupied rooms, so no space for more guests.
Re: Does infinity exist?
#7My 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.
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.
Re: Does infinity exist?
#8My 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…
Interesting
The two envelopes problem look like a "hard" Monty Hall problem, in the MH problem it's easy to see how swapping improves chances, since you're removing one bad option
Re: Does infinity exist?
#9My 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.
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…
You need to go and read up on the transfinite numbers. Swizec is talking about what happens when you deal with a certain sort of infinity (a countable infinity) where there's a one-to-one mapping between the hotel rooms and the numbers.
In the transfinite numbers things that at first seem unintuitive happen, e.g.:
1. There are the same number of integers as there are even numbers. And there are the same number of integers as there are odd numbers.
2. There are the same number of rational numbers (fractions) as there are integers.
3. There are more real numbers than integers.
Re: Does infinity exist?
#10My 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
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.