I am trying to show that field of all algebraic reals over $\mathbb{Q}$ has infinite degree. I guess that $$1,\sqrt{2},\sqrt[3]{2}, \sqrt[4]{2}, ...$$
are lineary independent but can't prove it.
2026-04-24 09:47:04.1777024024
Field of all algebraic reals over $\mathbb{Q}$ has infinite degree
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Perhaps simpler:
$$\forall\,n\in\Bbb N\;,\;\;[\Bbb Q(\sqrt[n]2):\Bbb Q]=n$$