Hilbert’s Hotel

Link: Hilbert’s Hotel

I love this Waylay comic about Hilbert’s Hotel. She does a beautiful job of explaining the paradox succinctly, and of tapping into the sense of human (nonmathematician) frustration with the whole deal at the same time. It’s an old favorite of mine.

There’s more on Hilbert’s Hotel at wikipedia. The classic version is: a hotel has an infinite number of rooms, and a person is staying in each room. A new guest arrives and is given a room. How is this possible?

Here’s a harder version: the infinite hotel across the street has a power outage, and sends all their (infinite) guests over to Hilbert’s hotel for the night. How do you give all of them rooms as well?