The Hilbert Hotel is a set of entertaining, and perhaps mind-boggling, examples illustrating arithmetic involving infinity. I forgot to mention it, but you may notice a phenomenon similar to Galileo's Paradox (see Part 2 of this series of videos) embedded in these examples. There is a deeper issue behind the Hilbert Hotel examples and Galileo's Paradox concerning the countability of elements in infinite sets. I will explain this is a future video.