Exercise 2.4.5: Suppose a Cauchy sequence {π₯π} β π=1 is such that for every π β β, there exists a π β₯ π and an π β₯ π such that π₯π < 0 and π₯π > 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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Step 1: Let (x_n) be a Cauchy sequence with the property that for every M in N there exist indices k,n >= M with x_k < 0 and x_n > 0. Show moreβ¦
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