At high school back in 1984, my year 9 math teacher (Larry Doolan) read us excerpts from "Stories about Sets" by N. Ya. Vilenkin (1968) [0].
The book's first story is about a hotel with an infinite number of rooms. It is fully booked, then one new guest arrives. Fortunately a solution is found. Then an infinite number of new guests arrive. After some head-scratching, a clever solution is found. Finally an infinity of infinite numbers of new guests arrive. And a lot of head-scratching, an even cleverer solution is still found!
The book's first story is about a hotel with an infinite number of rooms. It is fully booked, then one new guest arrives. Fortunately a solution is found. Then an infinite number of new guests arrive. After some head-scratching, a clever solution is found. Finally an infinity of infinite numbers of new guests arrive. And a lot of head-scratching, an even cleverer solution is still found!
[0] https://books.google.co.uk/books/about/Stories_About_Sets.ht...