Show that a finite group of guests arriving at Hilbert’s fully occupied Grand Hotel can be given rooms without evicting any current guest.

Solution: Step 1 : In this problem we have to prove that a finite group of guests arriving Hilbert’s fully occupied Grand Hotel can be given rooms without evicting any current guest. In the problem clearly given that finite group of guest arriving Hilbert’s fully occupied Grand Hotel and it is taken as 1,2,3,4,..............n There are numbers of guests in the hotel.So n number of rooms are required to accommodates the guest.First we do to arrange the current guest in room 1 to room (n+1) And shift the guest in room down to n.Similarly arrange the room to shift the guest in room 2 to room (n+2)And shift the one in room room down to the n.Again continuing this to 3,4,5,....... to n roomsafter n new guest are accommodates the process will complete.Hence use this way to arriving the guest in Hilbert’s fully occupied Grand Hotel can be given rooms without evicting any current guest.