Proving C is the Smallest Constructible Numbers Subfield with a>0 Property

  • Thread starter Thread starter Dragonfall
  • Start date Start date
  • Tags Tags
    Numbers
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
1 reply · 2K views
Dragonfall
Messages
1,023
Reaction score
5

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?
 

Discussion

Physics news on Phys.org
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?