The Grand Hotel

One of my favorite mathematics stories/folktales/thought experiments/jokes is that of David Hilbert's Grand Hotel, where Hilbert is of course the renowned mathematician you may know of already. Despite its appearance as just a rather strange mathematical folktale, it's based around true, yet counterintuitive mathematical properties of infinite sets. Though the story has many different versions by many authors, you can read my rendition of it below.

Source