Question: 1 Let X be the set of infinite sequences a = (ai)ien of real numbers such that |ai| < . For a = (ai)ieN

$(1) Let ( X ) be the set of infinite sequences ( a=left(a_{i}ight)_{i in mathbb{N}} ) of real numbers such that ($

1 Let X be the set of infinite sequences a = (ai)ien of real numbers such that |ai| < . For a = (ai)ieN and b = (bi)ien in X, define and d(a, b): Is da metric? Why? [Justify your assertion with a proof or a counterexample.] 2 Let X be the set of all functions of R into R that are continuous on the unit interval [0, 1]. For f, g E X, define (ai)ieN and b lai - b| i=1 Is d a metric? Why? ||*|| = (S |f(x)| dx d(f, g) = || f g||. Is da metric? Why? [Justify your assertion with a proof or a counterexample.] 3 Fix a real number p 1, and let X be the set of infinite sequences a = (ai)ien of real numbers such that a P < 0. For a = (bi)ieN in X, define = 1/1/20 d(a, b) = |ai - bi|P i=1 1/1/201 -^/^)

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