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## Main Question or Discussion Point

Well first hello, I'm not really into physics, learning computer science at uni atm. However wanted to get something off my mind.

Was browsing wikipedia a while ago and came across Hilbert's Paradox, the idea that a hotel with infinite rooms that are all full can still accept new guests by shifting guests over. It also said this (quoted from the wikipedia page):

http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

Anyway it is my thought that this is not true, the hotel with infinite rooms that are all full cannot accept more guests. My reasoning is that there are infinite rooms and they all exist already. Any room that exists is occupied. Any guest you make leave a room for another guest is then means there is infinity +1 guests, for each new guest there is another left without a room. Or for each new guest there is a series of infinite room swaps with a guest always without a room. Or each new guest already has a room as they are a part of the infinitely many guests.

Other thought is to view the hotel as a set, each guest as a dot, each dot is on a point (a room) in the set. The set has infinite points but you can't add points from outside the set, the set is already all points. So you can't add any more dots (aka guests) to this set as every point (aka room) already has a dot.

Anyway thoughts on my ramblings here?

Was browsing wikipedia a while ago and came across Hilbert's Paradox, the idea that a hotel with infinite rooms that are all full can still accept new guests by shifting guests over. It also said this (quoted from the wikipedia page):

*"This provides an important and non-intuitive result; the situations "every room is occupied" and "no more guests can be accommodated" are not equivalent when there are infinitely many rooms."*http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

Anyway it is my thought that this is not true, the hotel with infinite rooms that are all full cannot accept more guests. My reasoning is that there are infinite rooms and they all exist already. Any room that exists is occupied. Any guest you make leave a room for another guest is then means there is infinity +1 guests, for each new guest there is another left without a room. Or for each new guest there is a series of infinite room swaps with a guest always without a room. Or each new guest already has a room as they are a part of the infinitely many guests.

Other thought is to view the hotel as a set, each guest as a dot, each dot is on a point (a room) in the set. The set has infinite points but you can't add points from outside the set, the set is already all points. So you can't add any more dots (aka guests) to this set as every point (aka room) already has a dot.

Anyway thoughts on my ramblings here?