If you want to see the transfinite ordinals, then check out the Vsauce video "How To Count Past Infinity".
   • How To Count Past Infinity  

Here is Simon Pampena's Numberphile video about algebraic and transcendental numbers.
   • Transcendental Numbers - Numberphile  

My personal favourite way to order and count the rationals.
   • Infinite Fractions - Numberphile  

Watch James Grime show that the reals are uncountably infinite.
   • Infinity is bigger than you think - N...  

Here's what Mathsworld has to say:
http://mathworld.wolfram.com/OrdinalN...
http://mathworld.wolfram.com/Cardinal...

Here is a good English translation of Cantor's 1874 paper "On a Property of the Class of all Real Algebraic Numbers".
https://srjcstaff.santarosa.edu/~joma...


CORRECTIONS
- The polynomial which first appears at 3:40 has "n+1" which should be "n-1".
- Not all complex numbers are algebraic: only some of them are. I phrased this in an ambiguous way.
- Let me know if you spot anything else!


Thanks to my Patreon supports who do support these videos and make them possible. Here is a random subset:

Susan Moury
Bruce Patterson
Derek Chandler
Facundo Gonçalves Borrega
Scott Robinson

Support my channel and I can make more videos:
  / standupmaths  


Music by Howard Carter
Filming and editing by Matt Parker
Design by Simon Wright


MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
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