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Math Help - Real Analysis

  1. #1
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    Question Real Analysis

    Let Xn be a series of real numbers. Show that lim (n going to infinity)inf (-Xn)=-lim (n going to infinity)sup Xn.


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  2. #2
    Super Member girdav's Avatar
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    You have to show that \liminf_{n\to \infty} \left(-x_n\right)= -\limsup_{n\to \infty} \left(x_n\right)?
    Use \liminf_{n\to \infty}a_n = \sup_{n\in \mathbb N}\inf_{m\geq n}a_n and the result \sup_k \left(-a_k\right) = -\inf_k\left(a_k\right)
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  3. #3
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    You must returen to :

    Introduction To Real Analysis , By Robert Balrtle .
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