When infinity appears, making room stops being a question of gaps and becomes a question of order. This problem has the rare joy of ideas that seem impossible and yet fit entirely on one line.
Hilbert II's Hotel
Riddle statement
A hotel has infinitely many rooms numbered 1, 2, 3, …, and they are all occupied.
An infinite queue of new guests now arrives, numbered \(g_1, g_2, g_3, \dots\).
How can you accommodate them all?