Bounded Sequences, Metrics and Completeness
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Let X be the set of all bounded sequences of real numbers. If x=(a_k) and y=(b_k) let d be the metric funtion defined by d(x,y)=sup{|a_k - b_k|}
(note _ denotes subscript)
Show that the metric space defined above is complete.
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Proof:
We consider a sequence in , where . The sequence converges ...
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