Question: Exercise 2.6.5. Consider the following (invented) definition: A sequence (sn) is pseudo-Cauchy if, for all > 0, there exists an N such that if n

Exercise 2.6.5. Consider the following (invented) definition: A sequence (sn) is pseudo-Cauchy if, for all > 0, there exists an N such that if n N, then |sn+1 sn| <. Decide which one of the following two propositions is actually true. Supply a proof for the valid statement and a counterexample for the other. (i) Pseudo-Cauchy sequences are bounded. (ii) If (xn)and (yn) are pseudo-Cauchy, then (xn + yn) is pseudo-Cauchy as well.

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