Explore BrainMass

Explore BrainMass

    Bounded Real Sequences and Metrics

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Let X be the set of all bounded real sequences ... (SEE ATTACHMENT FOR COMPLETE QUESTION) ... For points x = {x1,,x2,x3...} and y = {y1,y2,y3...} in X define:
    d(x,y) := SUP |xk-yk|.
    (k less than or equal to 1)
    Prove that d is a metric (remember to explain why d(x,y) is finite!)

    (Please explain in your own words how the proof works. If you use a theorem, please state what it is and if possible, where you got it).

    © BrainMass Inc. brainmass.com September 26, 2022, 8:48 pm ad1c9bdddf


    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.


    First of all, we will show that d(x,y) = finite.
    Let Mx >0 so that

    Now, we need to check all the axioms of the metric:
    This is obvious because of the properties of module:

    Solution Summary

    Bounded Real Sequences and Metrics are investigated.