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Lex Fridman

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96176 total appearances
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Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

Oh, gosh.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

What's that proof look like?

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

How do you even begin?

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

I'm going to have to try to find a hole in that proof because there's a lot of baked in in the word interesting.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

But yeah, that's beautiful.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

That doesn't say anything about the transcendental numbers, about the real numbers.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

Sure.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

You've masterfully avoided the question.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

You basically said, I love all numbers.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

Yeah, basically.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

That's my intention.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

Back to Cantor's argument.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

Let's go.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

And so it's a kind of proof by construction.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

You beautifully got rid of the zeros and the nines, therefore we don't need to even consider that, and the proof still works.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

Exactly.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

Can we just step back a little bit?

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

This infinity crisis led to a kind of rebuilding of mathematics.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

So it would be nice if you lay out the things that resulted in.

Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

So one is set theory became the foundation of mathematics.

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