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IntroAnalysis

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## Homework Statement

If the absolute value of a sequence, a

_{n}converges to absolute value of A, does sequence, a

_{n}necessarily converge to A?

## Homework Equations

convergence: a sequence { an}n=1-->infinity, converges to A є R (A is called the limit of the sequence) iff for all є > 0, there exists an N є Natural, for all n[itex]\geq[/itex] N (│an - A│< є ).

Also, know that │ │a│ - │b││ [itex]\leq[/itex] │a - b│

## The Attempt at a Solution

I've been trying to find a counterexample, but so far I haven't been able to. Any suggestions on this proof?