I'm starting to study Cauchy sequences, could someone give an example of a sequence in R that is Cauchy with some metric but it is not with the Euclidean metric?
2026-03-28 20:05:41.1774728341
Cauchy sequences depending on the metric
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The following is a classic: take $x_n=n$ and the metric $d(x,y)=|\arctan(x)-\arctan(y)|$.