This is a very interesting video on the Infinite Hotel Paradox from Youtube. One of the best videos on the mysterious Infinity that I have ever watched. Do check it out!

The Infinite Hotel, a thought experiment created by German mathematician David Hilbert, is a hotel with an infinite number of rooms. Easy to comprehend, right? Wrong. What if it’s completely booked but one person wants to check in? What about 40? Or an infinitely full bus of people? Jeff Dekofsky solves these heady lodging issues using Hilbert’s paradox.

Lesson by Jeff Dekofsky, animation by The Moving Company Animation Studio.

Source: http://en.wikipedia.org/wiki/Hilbert’s_paradox_of_the_Grand_Hotel

**Hilbert’s paradox of the Grand Hotel** is a veridical paradox (a valid argument with a seemingly absurd conclusion, as opposed to a *falsidical paradox*, which is a seemingly valid demonstration of an actual contradiction) about infinite sets meant to illustrate certain counterintuitive properties of infinite sets. It was first described by George Gamow in his 1947 book One Two Three … Infinity and jokingly attributed to David Hilbert. (Wikipedia)

Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, insight, and brilliant illustrations.