Other number systems | Complex numbers episode 4

Video Description

#complexnumbers #quaternions #numbersystem #algebra Beyond the complex numbers, there are many other higher-dimensional number systems. We briefly look at some of the most famous ones, such as quaternions, octonions, Gaussian integers and more. Please consider supporting our channel on Patreon: https://www.patreon.com/user?u=86649007 Oops: At 5:40, I made a mistake. It should of course say "4+1=5". And here are some links where you can continue your research: [ALEPH0] https://www.youtube.com/watch?v=4m_EaWA08H0 In the Gaussian integers, the number 5 is no longer prime. A beautiful video by Aleph0. [3B1B 1] https://www.youtube.com/watch?v=NaL_Cb42WyY One of my favorite math videos ever. It uses Gaussian integers and their prime factorization to prove a formula for the number pi. [PENN 1] https://www.youtube.com/watch?v=ceaNqdHdqtg Michael Penn: The dual numbers. Some useful wikipedia links: https://en.wikipedia.org/wiki/Dual_number https://en.wikipedia.org/wiki/Split-complex_number https://en.wikipedia.org/wiki/Hyperreal_number https://en.wikipedia.org/wiki/Surreal_number https://en.wikipedia.org/wiki/P-adic_number https://en.wikipedia.org/wiki/On_Numbers_and_Games 0:00 Introduction 0:44 Field extensions 4:04 Gaussian integers 6:02 Some exotic number systems 8:14 Higher-dimensional number systems 10:28 Complex numbers are not ordered 12:08 Conclusion This video is published under a CC Attribution license ( https://creativecommons.org/licenses/by/4.0/ )