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Constructible Numbers

  • Thread starter Dragonfall
  • Start date
  • #1
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Homework Statement



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].


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?
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
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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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