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© Copyright 2000, Jim Loy
The Hotel Infinity is never full because it has infinitely many rooms. There is always room for any number of new guests. I think they use alternate dimensions in some way. One day, the Infinite Convention came to town, and they fit nicely into the Hotel Infinity, even though there were already guests staying there. Assume that there were already 100 guests, then the Infinite Convention moved into rooms 101, 102, 103, etc. No problem. Then one more person moved in. Again, no big problem, the management just asked the Infinite Convention to move into the next highest room (101 to 102, 102 to 103, etc.), and the new guest moved into the vacated room 101. Then Another Infinite Convention came to town. Was there room for them at the Hotel Infinity? Certainly. The management asked every guest to double their room number and move into that room (1 to 2, 2 to 4, 3 to 6, etc). That freed up infinitely many rooms for the Another Infinite Convention, who moved into the odd numbered rooms. I recommend the Hotel Infinity. I was able to stay there even though two conventions were in town simultaneously.
I have seen the Hotel Infinity described in a couple of books. One of them was aha! Gotcha - by Martin Gardner.