**Here at the Hotel de Hilbert, there are always vacancies!**

In 1925 Hilbert presented an infinity paradox that became better known as the Hilbert Hotel.

There are infinite guests in this hotel and it is packed, but whenever a customer arrives the manager asks guests to jump from room to room next door. Like this:

The guest of the room **1** jump to the room **2**

The guest of the room **2** jump to the room **3**

…

The guest of the room **no** jump to the room **n + 1 **

So the paradox is that although it is always crowded, there are always vacancies at the Hotel de Hilbert.