PlanetMath: every ordered field with the least upper bound property is isomorphic to the real numbers

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every ordered field with the least upper bound property is isomorphic to the real numbers

(Theorem)

Let $F$ be an ordered field. If $F$ satisfies the least upper bound property then $F$ is isomorphic as an ordered field to the real numbers $\mathbb{R}$

"every ordered field with the least upper bound property is isomorphic to the real numbers" is owned by archibal.

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Attachments:: proof that every ordered field with the least upper bound property is isomorphic to $\mathbb{R}$ (Proof) by mps

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AMS MSC:	12D99 (Field theory and polynomials :: Real and complex fields :: Miscellaneous)
	26-00 (Real functions :: General reference works )
	54C30 (General topology :: Maps and general types of spaces defined by maps :: Real-valued functions)

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