Infinity

As I pondered this topic, a simple google search came up with an interesting story about a Hotel Infinity. It was a bit on the long side but was very interesting and relevant to this topic. Here is the link if you are interested: http://www.c3.lanl.gov/mega-math/workbk/infinity/inhotel.html

I also came across a shorter story that focused on infinity that had a similar premise as your hotel story. The story is as follows:

A very large mathematical convention was held in Las Vegas. The conventioneers filled two hotels, each with an infinite number of rooms.The hotels were across the street from each other and were owned by brothers. One evening, while everyone was out at a bar-b-que, one of the hotels burned to the ground. The brothers got together and worked out a plan. In the remaining hotel, they moved all guests to twice their room number -- room 101 moved to 202, room 1234 moved to room 2468, etc. Then all the odd number rooms were empty, and there were an infinite number of odd rooms. So the guests from the other hotel moved into them. I really liked this story because it made me think. At first i thought it was impossible but since there is no end to infinity, I realized that it is actually very possible, as long as you can build a hotel with an infinite number of rooms.