Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Why why why (tiny limsup proof)

  1. May 11, 2007 #1

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper

    Don't they pretty much say the same thing?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook