- #1
annawells
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Homework Statement
Let K be the subfield of all constructible numbers in C
Let A be the subfield of all algebraic numbers in C
Is the field extension A:K finite?
The Attempt at a Solution
I don't know where to start! I have read and understood proofs that all constructible numbers are algebraic. I can think of some algebraic numbers which are not constructible, such as cube root of 2, coming from the equation (x^3)-2.
But I can't think how to go about seeing if there are a finite amount of such numbers?
please point me in the right direction! :)