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

2018-09-26

[public] 154K views, 5.92K likes, 73.0 dislikes audio only

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

Here is Simon Pampena's Numberphile video about algebraic and transcendental numbers.

My personal favourite way to order and count the rationals.

Watch James Grime show that the reals are uncountably infinite.

Here's what Mathsworld has to say:

Here is a good English translation of Cantor's 1874 paper "On a Property of the Class of all Real Algebraic Numbers".

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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MATT PARKER: Stand-up Mathematician