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Math Help - lim sup

  1. #1
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    lim sup

    Let (x_n) be a bounded sequence. For each n \in \mathbb{N} , let y_n=x_{2n} and z_n=x_{2n-1}. Prove that
    \limsup{x_n}=\max({\limsup{y_n},\limsup{z_n}}).

    I tried using the identity \max(x,y)=\frac{1}{2}{(x+y-|x-y|)}, but it can't seem to work... can anyone help me out?
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  2. #2
    Super Member girdav's Avatar
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    Re: lim sup

    \limsup_n x_n=\lim_n\sup_{k\geq n}x_k=\lim_n\max (\sup_{2k\geq n}x_{2k},\sup_{2k+1\geq n}x_{2k+1}). Put the \lim into the \max to get the result.
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