Ordinals vs Cardinals (and how many algebraic numbers are there?)

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 - Number...  

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!


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Susan Moury
Bruce Patterson
Derek Chandler
Facundo Gonçalves Borrega
Scott Robinson

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MATT PARKER: Stand-up Mathematician
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