[Step-by-Step] For each of the following statements determine whether the statement is true or false. If the statement is false give a counterexample. If
Question: For each of the following statements determine whether the statement is true or false. If the statement is false give a counterexample. If the statement is true, provide a brief justification.
- A subsequence of a bounded sequence is bounded
- A subsequence of a monotone sequence is monotone.
- A subsequence of a convergent sequence is convergent.
- A sequence converges if it has a convergent subsequence.
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