Hilbert’s Infinite Hotel Paradox is a thought experiment which demonstrates that when we enter the realm of actual infinity, we must check our intuitions at the door. In this video, we look at Hilbert's Hotel Paradox and then consider a sequel to the story, where the hotel manager from the Potentially Infinite Hotel tries to bring his number system to the Actually Infinite Hotel. Contents: Intro: 0:00 Hilbert's Hotel: 0:13 Infinite Hotel Sequel: 1:47 #InfiniteHotel #Paradox