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

Season 2 Episode 15 | 13m 02s

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?

Aired: 08/28/18
Extras
Can you save the target from his assassin in a square room with bouncy walls?
Can you stack four colored cubes so that each color only shows once on each side?
Set theory is the foundation of all of mathematics. How does it handle infinity?
When you think about math, what do you think of knots? Probably... knot.
In SET, what is the maximum number of cards you can deal that might not contain a SET?
What shape do you most associate with a standard analog clock? Circle or... torus?
Could you explain numbers to someone without using the notion of a number?
If Fermat had a little more room in his margin, what proof would he have written there?
In the physical world, objects are made of simpler parts. What are numbers made of?
Here we break down Asymmetric crypto and more.
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Can you save the target from his assassin in a square room with bouncy walls?
Can you stack four colored cubes so that each color only shows once on each side?
Set theory is the foundation of all of mathematics. How does it handle infinity?
When you think about math, what do you think of knots? Probably... knot.
In SET, what is the maximum number of cards you can deal that might not contain a SET?
What shape do you most associate with a standard analog clock? Circle or... torus?
Could you explain numbers to someone without using the notion of a number?
If Fermat had a little more room in his margin, what proof would he have written there?
In the physical world, objects are made of simpler parts. What are numbers made of?
Here we break down Asymmetric crypto and more.