Show the algebraic closure $\bar{\mathbb{Q}}$ is not even finitely generated over the field $\mathbb{Q}$
I'm not sure how to go about this..
2026-03-25 20:59:54.1774472394
Algebraic closure not even finitely generated over base field
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Hint: Show that for any natural $n$, there is an algebraic extension of $\Bbb Q$ of degree (at least) $n$. And any finitely generated algebraic extension has some finite degree.