I have very little idea about how to approach this question. It doesn't make any sense to me how this can be Cauchy. Any insight into it would be greatly appreciated.
2026-04-06 17:49:11.1775497751
A new type of Cauchy sequence
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HINT: Suppose that $\langle a_n:n\in\Bbb N\rangle$ is Daudhy, and let $\epsilon>0$. There is a $T\in\Bbb N$ such that $d(a_j,a_k)<\frac{\epsilon}2$ whenever $T<j<2T<k$. Use the triangle inequality to show that $d(a_j,a_k)<\epsilon$ whenever $j,k>2T$ and conclude that the sequence is Cauchy.