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 $\epsilon$ is an arbitrary positive number, then there exists in $K$ an element $y$ which satisfies the conditions