104-hw5 - ( h x i i , h y i i ) = sup {| x j-y j | : j N }...

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Math 104 - Lecture 1 - Problem Set 5 Due Tuesday, July 20, 2010 Do the following exercises from the book: 2.2, 2.12, 2.26, 2.32, 2.34 1. Let B be the set of all bounded sequences or real numbers h x 1 ,x 2 ,... i . For h x i i , h y i i ∈ B , define d
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Unformatted text preview: ( h x i i , h y i i ) = sup {| x j-y j | : j N } . (a) Prove that d is a metric for B . (b) Let F = {h x i i B : for all j N , | x j | 1 } . Prove that F is a closed subset of B ....
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