Lex Fridman

So to just say one more time, the hotel is full.

And then you could still squeeze in one more, and that breaks...

the traditional notion of mathematics and breaks people's brains about when they try to think about infinity, I suppose.

This is a property of infinity.

You separate the hotel into even and odd rooms and you squeeze in the new bus people into the odd rooms and the previous occupants go into the even rooms.

And by doing so, you have now shoved in an infinity into another infinity.

And prime factorization is every single number can be...

decomposed into the atoms of mathematics, which is the prime numbers.

You can multiply them together to achieve that number.

And that's prime factorization.

You're showing three and five are both prime numbers.

Odd.

So through this magical formula, you can deal with this train, infinite number of cars, with each car having infinite number of seats.

Exactly right.

Have you been able to sort of internalize a good intuition about countable infinity?

Because that is a pretty weird thing.

You can have a countably infinite set of countably infinite sets, and you can shove it all in, and it still is a countable infinite set.

Yeah, it's a really nice visual way to think about it.

You just zigzag your way across the grid to make sure everybody's included.

That gives you kind of an algorithm for including everybody.