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Homework Help: Lim inf/sup innequality question

  1. Mar 12, 2009 #1
    x_n and y_n are bounded
    lim sup x_n+lim sup y_n>=lim x_r_n+lim y_r_n

    this is true because there presented sub sequences converge to the upper bound of x_n and y_n .
    the sum of limits is the limit of sums so we get one limit
    and the of two convergent sequence is one convergent sequence
    this is true because the sequence is constructed from a convergent to the sup sub sequences
    so they equal the lim sup of x_n+y_n

    now i need to prove that
    limsup(x_n+y_n)=>liminf x_n+limsup y_n

    i tried:
    limsup(x_n+y_n)=limsup x_n+limsup y_n=>liminf x_n+limsup y_n
    lim sup i always bigger then lim inf

    so its true

    did i solved it correctly?
    Last edited: Mar 12, 2009
  2. jcsd
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