Let $n\in\mathbb N$. then, is there a subfield of $\mathbb C$ such that $[\mathbb C:K]$= $n$ ?
if $n$ = 1,2, then answer is yes. But I don't know if $n$ is larger than 2.
How do I proceed more?
Thanks!
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1Look at this: http://math.stackexchange.com/questions/202072/finiteness-of-the-algebraic-closure?s=3|0.8198 – P Vanchinathan Jan 02 '16 at 08:22
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Thanks. That means any subfield K of C is of [C:K] = 1 or 2 or infinity, am i right? – nicksohn Jan 02 '16 at 08:39