No, because once the first client moves, the first room is free for the new guest, even though the whole process of moving hasn't finihsed yet, and in fact will never be finished. You will end up having infinite "waves" of moving clients.
assume that no guests have possession, and that every room has a door to the previous and next rooms
My point is, there are intermediate states when you can't strictly say the hotel is full and that every occupant has a room, i.e. one-to-one relation. In your scenario, if you start from the first room, you will always have one room with two occupants, which is against the rules, or in my scenario there will always be one homeless dude.
I understand this is an abstract situation anyway, which can not be experimentally reproduced (for one, it would take infinite time to build this hotel and we'll never see it finished), which leads to the next point:
Does someone standing silently behind you cease to exist until you turn around?
You can never be sure about anything unless you observe it using your own senses and possibly some equipment in the middle. (And it gets even worse in the quantum world, but let's forget that for a moment.) So strictly speaking, when you don't see the person behind you, you can only make a prediction/hypothesis that if you turn around you will see that person again. It's based on some laws of physics suggesting that a person can't disappear, say, in one nanosecond. But hypothesis is just a hypothesis, and it's not observation of reaality, e.g. a fact.
Back to infinities. In the physical world all kinds of infinite values are defined through either infinite distance or infinite time, including both infitely big or small, i.e. ∞ and 1/∞. Space and time are closely related though, because in order to measure a distance you need "some" time, and obviously, to measure or observe infinite distance you need infinite time. Which is not possible for us, humans and therefore infinity is just a hypothesis, and I'm afraid will always be. (Always? You mean, for infinitely long time? :)
Curiously, for some reason I started thinking about infinities this morning and here you go, a post at YCNews.
So strictly speaking, when you don't see the person behind you, you can only make a prediction/hypothesis that if you turn around you will see that person again. It's based on some laws of physics suggesting that a person can't disappear, say, in one nanosecond. But hypothesis is just a hypothesis, and it's not observation of reaality, e.g. a fact.
There is a pretty good Overcoming Bias post on why this is wrong:
So he understands that when we lose sight of that photon, from that point on our knowledge about it becomes a hypothesis based on laws of physics. Unfortunately laws of physics are neither 100% accurate nor complete - there may be some laws not discovered and formulated yet and even those discovered never give you 100% accuracy in making predictions.
However, we are talking about infinities, which is a different kind of beast. My main thesis is that in order to measure infinite distance you need infinite time, which we simply don't have at our disposal, and thus infinity in any of its form can't be observed in principle.
No, because once the first client moves, the first room is free for the new guest, even though the whole process of moving hasn't finihsed yet, and in fact will never be finished. You will end up having infinite "waves" of moving clients.
assume that no guests have possession, and that every room has a door to the previous and next rooms
My point is, there are intermediate states when you can't strictly say the hotel is full and that every occupant has a room, i.e. one-to-one relation. In your scenario, if you start from the first room, you will always have one room with two occupants, which is against the rules, or in my scenario there will always be one homeless dude.
I understand this is an abstract situation anyway, which can not be experimentally reproduced (for one, it would take infinite time to build this hotel and we'll never see it finished), which leads to the next point:
Does someone standing silently behind you cease to exist until you turn around?
You can never be sure about anything unless you observe it using your own senses and possibly some equipment in the middle. (And it gets even worse in the quantum world, but let's forget that for a moment.) So strictly speaking, when you don't see the person behind you, you can only make a prediction/hypothesis that if you turn around you will see that person again. It's based on some laws of physics suggesting that a person can't disappear, say, in one nanosecond. But hypothesis is just a hypothesis, and it's not observation of reaality, e.g. a fact.
Back to infinities. In the physical world all kinds of infinite values are defined through either infinite distance or infinite time, including both infitely big or small, i.e. ∞ and 1/∞. Space and time are closely related though, because in order to measure a distance you need "some" time, and obviously, to measure or observe infinite distance you need infinite time. Which is not possible for us, humans and therefore infinity is just a hypothesis, and I'm afraid will always be. (Always? You mean, for infinitely long time? :)
Curiously, for some reason I started thinking about infinities this morning and here you go, a post at YCNews.