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Math · Advanced Math
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Exercise 2. Let X be the subset of 1°0 consisting of sequences of real numbers that have only finitely many non-zero entries: X (anhel C R : xn 0 for only finitely many n > 1 We equip X with the doo metric: for any two points x- [lnn>1 and y - {ynn1 in X, we define d,e(x, y) = sup |xn-Yn 1 n 1 (a) Show that the sequence (rk1 C X given by (k)1 is a Cauchy sequence. (b) Conclude that (X, doo) is not a complete metric sp

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