The Infinite Hotel Paradox - Jeff Dekofsky
- 24,102,571 Views
- 32,574 Questions Answered
- TEDEd Animation
Let’s Begin…
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.
Create and share a new lesson based on this one.
Additional Resources for you to Explore
The concept of infinity has fascinated humans since ancient
times.The first known reference comes
from the 5th 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 TED-Ed 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
Dennis Wildfogel also created an original TED-Ed 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

TED-Ed
Lesson Creator
New York, NY
If we were to try to fill the Real Number Infinite Hotel, what are some of the issues that we wil...
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.
More from Math In Real Life
36,346,054 Views
Mathematics
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem
Lesson duration 05:20
3,370,756 Views
4,832,037 Views
2,358,034 Views