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In this episode I'll explain about how/why there are different sizes of "infinity", including concepts such as Cantor's Diagonal Argument, the Aleph Numbers, the Continuum Hypothesis, and more!
0:00 - Intro
1:37 - How Many Square Numbers Are There?
2:51 - Surjective/Injective/Bijective Cats
6:03 - How Many Integers Are There?
7:28 - How Many Fractions Are There?
12:46 - How Many Real Numbers Are There?
13:36 - Cantor's Diagonal Argument
19:54 - The Hierarchy of Aleph Numbers
21:28 - The Continuum Hypothesis
24:51 - Outro
To my Combo Lords: Sorry that some recent episodes have taken a while to finish. I’ve been in the process of semi-moving houses and other personal things (see the livestream videos on my bonus @Domotro channel for some details). My next episode may also take a couple weeks, since it’ll be a long one about what I consider to be the most underrated concept in number theory. After that, I can hopefully get back to a quicker release schedule. In any case, thanks for watching!
Special thanks to all of my supporters on Patreon! (Supporting the show not only helps me keep improving my content, but also lets me avoid having any product placements from brands in episodes)
Evan Clark, Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, Dave Brondsema, and Chandler Smith!
If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: / comboclass
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If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com
In case anybody searches any of these terms to learn about them, some topics in this video include: countable vs. uncountable infinities, bijections and injective/sujective/bijective functions, the Aleph numbers like Aleph 0 and Aleph 1, Georg Cantor and Cantor's diagonal / diagonalization argument, the Continuum Hypothesis, and other topics related to "set theory" and different sizes/cardinalities of infinities.
This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.
Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.