(Answered) 1 show that if ann1infinity and bnn1infinity are equivalent

Statistics

1. Show that if (a_n)[n=1,infinity] and (b_n)[n=1,infinity] are equivalent sequences of rationals, then (a_n)[n=1,infinity] is a Cauchy sequence if and only if (b_n)[n=1,infinity] is a Cauchy sequence.

2. Let epsilon > 0. Show that if (a_n)[n=1,infinity] and (b_n)[n=1,infinity] are eventually epsilon-close, then (a_n)[n=1,infinity] is bounded if and only if (b_n)[n=1,infinity] is bounded.

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