# Proof Equivalent Cauchy Sequences

1) show that if (a_n)^infinity evaluated at n=1, and (b_n)^infinity evaluated at n=1 are equivalent sequences of rationals, then (a_n) ^infinity evaluated at n=1 is a Cauchy sequence if and only if (b_n)^infinity evaluated at n=1 is a Cauchy sequence.

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

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#### Solution Summary

This solution provides proof that a given sequence is a Cauchy sequence.

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