a) Let a X. Prove that if xn = a for every n N, then

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a) Let a ∈ X. Prove that if xn = a for every n ∈ N, then xn converges. What does it converge to?
b) Let X = R with the discrete metric. Prove that xn → a as n → ∞ if and only if xn = a for large
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