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A Hierarchy of Infinities | Infinite Series | PBS Digital Studios

2016-12-08

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There are different sizes of infinity. It turns out that some are larger than others. Mathematician Kelsey Houston-Edwards breaks down what these different sizes are and where they belong in The Hierarchy of Infinities.

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Written and Hosted by Kelsey Houston-Edwards

Produced by Rusty Ward

Graphics by Ray Lux

Made by Kornhaber Brown (www.kornhaberbrown.com)

Sources:

Proof that the real numbers are a bigger infinity than the natural numbers:

http://germain.its.maine.edu/~farlow/sec25.pdf

http://www.people.vcu.edu/~rhammack/BookOfProof/Cardinality.pdf

Thanks James Barnes and Iian Smythe!


BIJECTION
/youtube/video/i7c2qz7sO0I?t=98
there is no size of infinity between the natural numbers and the real numbers
/youtube/video/i7c2qz7sO0I?t=346
ZERMELO-FRAENKEL set theory w (ZFC)
/youtube/video/i7c2qz7sO0I?t=372
TOWER OF INFINITI
/youtube/video/i7c2qz7sO0I?t=428