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)
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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.