Lex Fridman

So can you speak to the uncountable infinities?

What are the integers and the real numbers, and what is the line that Cantor was able to find?

So let's talk about the real numbers.

What are the real numbers?

Why do they break infinity, the countable infinity?

Looking it up on perplexity, real numbers include all the numbers that can be represented on the number line, encompassing both rational and irrational numbers.

We've spoken about the rational numbers.

And the rational numbers, by the way, are by definition the numbers that can be represented as a fraction of two integers.

And we won't even go to the surreal numbers about which you have a wonderful blog post.

We'll talk about that a little bit later.

And again, going to perplexity, transcendental numbers are real or complex numbers.

They're not the root of any non-zero polynomial with integer or rational coefficients.

This means they cannot be expressed as solutions to algebraic equations with integer coefficients, setting them apart from algebraic numbers.

That's right.

So you could say that some of the sexiest numbers in mathematics are all transcendental numbers.

Absolutely, that's true.

Although, you know, I don't know, square root of two is pretty... All right, so it depends.

Beauty can be found in all the different kinds of sets.

Sorry to take that tangent, but what is your favorite number?

Do you have one?