(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove the Boundedness Theorem for Cauchy Sequences by a contrapositive argument.

2. Relevant equations

3. The attempt at a solution

If {an} is not bounded then {an} is not a cauchy sequence.

We will prove that {an} is not a cauchy sequence by showing that there exists an ε>0 so that for every pos. int. N there exists an n,m>N so that abs(an-am)≥ε.

Set ε=1

Consider positive N arbitrary.

Since by hypothesis {an} is not bounded to mean for every B there exists an n so that abs(an)>B. Choose such an n.

This is where I am stuck, how do I find/choose an m? Also how do I get the inequalities to work out at the end?

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# Intro to Analysis (Boundedness of Cauchy)

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