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    Bounded Real Sequences and Metrics

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    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).

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    https://brainmass.com/math/algebra/bounded-real-sequences-metrics-34598

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    Solution:

    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:
    1)
    This is obvious because of the properties of module:
    ...

    Solution Summary

    Bounded Real Sequences and Metrics are investigated.

    $2.49

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