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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 - 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/ Maths book: http://makeanddo4D.com/ Nerdy maths toys: http://mathsgear.co.uk/