Why why why (tiny limsup proof)

  1. May 11, 2007 #1

    quasar987

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    There's a "theorem" in my book that says if x is a cluster point of {x_n}, then lim inf(x_n)[itex]\leq[/itex]x[itex]\leq[/itex]lim sup(x_n).

    The way the author proves it is a little bit extravagant. Why not just say "Let A be the set of all cluster points. Then, lim inf(x_n)=inf(A)[itex]\leq[/itex]x[itex]\leq[/itex]sup(A)=lim sup(x_n)."

    ???
     
  2. jcsd
  3. May 13, 2007 #2

    Dick

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    Don't they pretty much say the same thing?
     
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