Definition
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[0X0] Let \(I\) be a non-empty set, with at least two elements. Let \(X=\{ f:ββ I\} =I^β\) be the space of sequences. Let \(x,yβ X\). If \(x=y\) then we set \(d(x,y)=0\).Β 1 If \(xβ y\), we set
\begin{equation} c(x,y)=\min \{ nβ₯ 0, x(n)β y(n)\} \label{eq:c_ ultrametrica_ succ} \end{equation}
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to be the first index where the sequences are different; then we define \(d(x,y)=2^{-c(x,y)}\).