1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Cauchy sequence and convergeant diameters.

  1. May 5, 2013 #1
    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. jcsd
  3. May 5, 2013 #2
    ##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.
     
  4. May 5, 2013 #3
    That makes sense, thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Cauchy sequence and convergeant diameters.
Loading...