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Posted: **Wed Jul 06, 2022 12:04 pm**

: Let An Be A Real Sequence Prove Or Give A Counterexample To The Following Statement If An Is A Cauchy Sequence And 1 (18.6 KiB) Viewed 50 times

Let (an) be a real sequence. Prove or give a counterexample to the following statement: If (an) is a Cauchy sequence and f is a continuous function where f(an) is defined for all neN, then (f(an)) is a Cauchy sequence. (3 markah/marks)
Let (an) be a Cauchy sequence. Suppose the set S = {an neN} is finite. Show that there erists a positive integer N such that an an for all n ≥ N. (3 markah/marks)