By setting Cauchy constant you easily see how all Cauchy sequences in this space must look like. And to what values they converge.
Define the metric spaces with , the set of integers with the metric
Find sequence in this metric space such that it is cauchy but do not converge.
I understand I must find a sequence that takes only integer values but converge to non-integer. But how should I get it to be cauchy?
Thank you.