Cantor illustrated the concept of infinity for his students by telling them that there was once a man who had a hotel with infinite numbers of rooms and the hotel was fully occupied. Then one more guest arrived. So the owner moved the guest in room number one into room number two; the guest in room number two into number three; the guest in three in room four and so on. In that way room number one became vacant for the new guest.
What delights me about this story is that everyone involved, the guests and the owner, accept it as perfectly in order to carry out an infinite number of operations so that one guest can have peace and quiet in a room of his own. That is a great tribute to solitude.