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Let $k$ be a field and $x$ is transcendental over $k$. Can we construct a pseudo-cauchy sequence $(a_{i})$ convergent to $x$ with each $a_{i}$ is algebraic over $k$ and $k(a_{i})\subseteq k(a_{i + 1})$. Thanks

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  • $\begingroup$ Is your question whether such a $k$ and $x$ exist, or whether a sequence can be found for any given $k$ and $x$ of the form you describe? $\endgroup$
    – Yemon Choi
    Jan 11, 2013 at 1:19
  • $\begingroup$ @ Yemon, thanks. I am looking whether a sequence exist or not for any given $k$ and $x$. $\endgroup$
    – Rajnish
    Jan 11, 2013 at 2:49

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