How Big are All Infinities Combined? (Cantor's Paradox) | Infinite Series

How Big are All Infinities Combined? (Cantor's Paradox) | Infinite Series

Apr 23, 2021
|
23 views
Details
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? 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)

Comments
loading...