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# independence of valuations

Let $|\cdot|_{1}$, …, $|\cdot|_{n}$ be non-trivial (i.e., they all have also other values than 0 and 1) and pairwise non-equivalent valuations of a field $K$, all with values real numbers. If $a_{1}$, …, $a_{n}$ are some elements of this field and $\varepsilon$ is an arbitrary positive number, then there exists in $K$ an element $y$ which satisfies the conditions

$\displaystyle\begin{cases}|y-a_{1}|_{1}<\varepsilon,\\ \vdots\\ |y-a_{n}|_{n}<\varepsilon.\\ \end{cases}$ |

Related:

TrivialValuation, EquivalentValuations, WeakApproximationTheorem

Synonym:

approximation theorem

Type of Math Object:

Theorem

Major Section:

Reference

Parent:

Groups audience:

## Mathematics Subject Classification

11R99*no label found*

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