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Math Help - Convergent sequence proof

  1. #1
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    Convergent sequence proof

    Prove that if an converges to A, then |an| converges to |A|. Then prove or disprove the converse to this.

    Well...

    if an converges to A, then |an-A|<epsilon for n>=N. So do we just approach this first for an positive and then negative to show it converges to |A|. I don't know how to show this formally... I would say the converse is likely false since it could be negative.
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  2. #2
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    This is a well known inequality.
    \left| {\left| x \right| - \left| y \right|} \right| \leqslant \left| {x - y} \right|

    From that the proof is trivial.
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