1. Prove or give a counterexample.
(a) Every oscillating sequence has a convergent subsequence.
(b) Every oscillating sequence diverges.
(c) Every divergent sequence oscillates.
2. Prove or give a counterexample.
(a) Every bounded sequence has a Cauchy subsequence.
(b) Every monotone sequence has a bounded subsequence.
(c) Every convergent sequence can be represented as the sum of two oscillating sequences
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