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Exercise 2.4.5: Suppose that a Cauchy sequence {xn} is such that for every M ∈ N,...

Exercise 2.4.5: Suppose that a Cauchy sequence {xn} is such that for every M ∈ N, there exists a k ≥ M and an n ≥ M such that xk < 0 and xn > 0. Using simply the definition of a Cauchy sequence and of a convergent sequence, show that the sequence converges to 0.

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