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Homework Help: Constructible Numbers

  1. Mar 12, 2007 #1
    1. The problem statement, all variables and given/known data

    Show that the field C of constructible numbers is the smallest subfield of R with the property that [tex]a\in C, a>0 \Rightarrow \sqrt{a}\in C[/tex].


    3. The attempt at a solution

    Suppose there's a proper subfield of C' of C that has that property, then let [tex]a\in C-C'[/tex]. Somehow I must show that a is actually in C. Perhaps repeated squaring?
     
  2. jcsd
  3. Mar 12, 2007 #2

    Hurkyl

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    Maybe a different tactic would be useful?

    Let C' be the smallest subfield with that property. Can you prove C is a subfield of C', and that C has that property?
     
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