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Formally real field
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==Real closed fields== A formally real field with no formally real proper [[algebraic extension]] is a [[real closed field]].<ref name=R216>Rajwade (1993) p.216</ref> If ''K'' is formally real and Ξ© is an [[algebraically closed field]] containing ''K'', then there is a real closed [[Field extension|subfield]] of Ξ© containing ''K''. A real closed field can be ordered in a unique way,<ref name=R216/> and the non-negative elements are exactly the squares.
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