Exercise 16, § 8

Let K be a Henselian field with a valuation v of height 1. If L is an infinite separable algebraic extension of K, show that L cannot be complete with the valuation extending v (and also denoted by v). (Form a sequence $(x_p)$ of elements of L such that the degree $n_p$ of $x_p$ with respect to K tends to $+\infty$ and $v(x_{p+1} - x_p)$ is strictly greater than the valuations of the differences between $x_p$ and its conjugates with respect to K; show that the sequence $(x_p)$ is a Cauchy sequence which cannot converge in E, using Exercise 12 (b).)