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Math Help - Realy Analysis - Algebraic Limit Theorem #2

  1. #1
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    Realy Analysis - Algebraic Limit Theorem #2

    a. Show that if (bn) --> b, then the sequence of absolute values |bn| converges to |b|

    b. Is the converse of part a. true? If we know that |bn| --> b, can we deduce that (bn) --> b?
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  2. #2
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    Use this well known inequality: \left| {\left| x \right| - \left| y \right|} \right| \leqslant \left| {x - y} \right|.
    Part (a) follows at once.

    For part (b), consider \left( {b_n } \right) = \left( { - 1} \right)^n .
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  3. #3
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    Thanks Plato

    I just wanted to say thanks for responding to my question. Luckily I was able to locate the answers you listed in my notes from class. Unfortunately I stayed up all night completing this assignment.
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