The Infinite Hotel Paradox  Jeff Dekofsky

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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.
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The concept of infinity has fascinated humans since ancient times.The first known reference comes from the 5^{th} century B.C.E. Wikipedia presents many interesting facts and applications of the concepts of both potential infinity (as used in Calculus for example) and actual infinity (as used in Set Theory).
Dennis Wildfogel also created an original TEDEd lesson on the concept of actual infinity. You can watch it here.
Another great place to watch videos on infinity and other number related concepts is Numberphile.
Here are a few of their specific videos dealing with infinity, prime numbers, etc.:
http://numberphile.com/videos/countable_infinity.html
http://numberphile.com/videos/infinity_paradoxes.html
http://numberphile.com/videos/infinite_primes.html
http://numberphile.com/videos/zeno_paradox.html
In addition to online resources, there are also some outstanding books dealing with the concept of infinity. Here is a very short list that I would highly recommend:
The Infinite Book: A Short Guide to the Boundless, Timeless and Endless by John Barrow
The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity by Amir D. Aczel
To Infinity and Beyond: A Cultural History of the Infinite by Eli Maor
Why do numbers like the square root of 2 or pi, as well as other irrational (infinite decimal) numbers make a system difficult to design? Think about the systems that the manager used to fill the Natural Number Infinite Hotel. Can we adjust any of these to do the job?
Create and share a new lesson based on this one.
About TEDEd Originals
TEDEd Original lessons feature the words and ideas of educators brought to life by professional animators. Are you an educator or animator interested in creating a TEDEd original? Nominate yourself here »