# Homework Help: Cauchy sequence and convergeant diameters.

1. May 5, 2013

### gottfried

Suppose (an) is sequence in the metric space X and define Tn={ak:k>n} and diamT=sup{d(a,b):a,b elements of T}.

Prove that (an) is Cauchy if and only if diam Tn converges to zero.

In what metric spacee does Tn converge? I assumed in (ℝ,de) but this is confusing since the diam of T is measured using the metric of X.

2. May 5, 2013

### voko

$T_n$ is set in space X.

$\mathrm{diam} \ T_n$ are real numbers, and nothing is said what metric is to be used on them. Which probably means the "natural" Euclidean metric.

3. May 5, 2013

### gottfried

That makes sense, thanks.