New posts in Cauchy Sequences

Does convergence for Cauchy sequence fail only when the limit is not in the domain?

Can a Cauchy sequence converge for one metric while not converging for another?

What sequences are Cauchy in all metrics for a given topology?

Is this a valid convergence test (for sequences)?

Quasi-Cauchy sequences

Bounded sequence $\{a_n\}_n$ such that $a_n < \frac{a_{n−1} + a_{n+1}}{2}$. Is $\{a_n\}_n$ convergent?

My Proof: Every convergent sequence is a Cauchy sequence.

Showing that a totally bounded set is relatively compact (closure is compact)

If $|x_{n+1} - x_n| < \epsilon,$ is $(x_n) $ a Cauchy sequence?

How to prove that the both definition of completeness of $\mathbb{R}$ are equivalent?