What if there are infinitely many things?
This doubling trick opens up all the odd-numbered rooms - infinitely many of them - for the new guests.
If there's infinitely many universes, then surely there are other copies of you and me having this conversation.
There are infinitely many buses, and worse still, each one is loaded with an infinity of crabby people demanding that the hotel live up to its motto, “There’s always room at the Hilbert Hotel.”
There are infinitely many real numbers between any two distinct real numbers.
The integers divide the number line into infinitely many half-open intervals.