Partner Problem: The famous mathematician David Hilbert invented the notion of the Gran Hotel, which has a countably infinite number of rooms, each occupied by a guest. When a $n$ guest arrives at a hotel with a finite number of rooms, and all rooms are occupied, this guest cannot be accommodated without evicting a current guest. However, we can always accommodate a new guest at the Grand Hotel, even when all rooms are already occupied.

a$.$ How can we accommodate a new guest arriving at the fully occupied Grand Hotel withou removing any of the current guests?

Aeke $2$ guest to share one room if they