Thanks for this, this is a topic I've been curious about for a long time, but never knew how to learn about it without diving into a textbook. I'm reading thro

Thanks for this, this is a topic I've been curious about for a long time, but never knew how to learn about it without diving into a textbook. I'm reading through it now, and I'm confused by this statement: "Second, and more surprisingly, if you swap r_1 and r_2r, x_1 and x_2 also exchange places, seemingly contradicting Theorem 1!" Why is there any connection to theorem 1 here? We're talking about a radical, and theorem 1 is concerned with rational expressions.