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If there is a field $F$ that is a field reduction of the real numbers, that is $F(a)=\mathbb{R}$ for some $a$, let's also denote this $F=\mathbb{R}(\setminus a)$, then given $x \in \mathbb{R}$ is there a general method to determine whether $x$ is in $F$ or $x$ is in $\mathbb{R}\setminus F$ ?

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    The answer probably depends on how F is given... Can you describe F explicitly? I do not know a single example!2010-11-27
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    All you know is that F(a)=R, and anything you can deduce from that.2010-11-27

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