2018-03-23

[public] 116K views, 3.47K likes, 81.0 dislikes audio only

PBS Infinite Series

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi

Infinities come in different sizes. There’s a whole tower of progressively larger "sizes of infinity". So what’s the right way to describe the size of the whole tower?

Tweet at us! @pbsinfinite

Facebook: facebook.com/pbsinfinite series

Email us! pbsinfiniteseries [at] gmail [dot] com

Previous Episode:

The Geometry of SET

/youtube/video/zurpOBPt4LI

Check out the solution to the Geometry of SET challenge problem right here: https://bit.ly/2Ggpw1d

Talking about the sizes of infinite things is tricky in part because the word “infinite” is often used in two distinct ways -- to refer to the sets themselves, and also to refer to the *sizes* of those sets. In what follows, let’s try to keep as sharp a distinction as we can between infinite sets and infinite set *sizes*, because doing so will let me highlight an especially paradoxical feature about infinite sizing that I don't think gets enough coverage. The technical term for a “size”, infinite or otherwise, is “cardinality”, and I should probably use a term like “numerousness” or “numerosity” rather than “size” because the idea it tries to generalize is the notion of "how many". Still, I’m going to say “size” a lot in this episode just because it’s easier.

Written and Hosted by Tai-Denae Bradley

Produced by Rusty Ward

Graphics by Ray Lux

Assistant Editing and Sound Design by Mike Petrow and Linda Huang

Made by Kornhaber Brown (www.kornhaberbrown.com)

Thanks to Peleg Shilo, Anurag Bishnoi, and Yael Dillies for your comments on last week's episode:

/youtube/video/zurpOBPt4LI&lc=UgzxzGjWJh8Pra57LDR4AaABAg

/youtube/video/zurpOBPt4LI&lc=Ugx2lMNH6inRYiTGFSx4AaABAg

/youtube/video/zurpOBPt4LI&lc=UgzA2HK0J9ytm01lUex4AaABAg

Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.

Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!

And thanks to Mauricio Pacheco and Andrew Poelstra who are supporting us at the Lemma level!