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How to visualize these terms

  1. Dec 11, 2008 #1
  2. jcsd
  3. Dec 11, 2008 #2

    HallsofIvy

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    You have two sequences {xn} and {yn} and say that "by Bolzano-Weierstrasse", [itex]\underline{\lim_{n\rightarrrow \infty}x_n}\le \lim_{n\rightarrow\infty}x_{N_n}[/itex].

    I will guess, from your other posts, that the underline is meant to be "lim inf" but what is [itex]x_{N_n}[/itex]? An arbitrary subsequence of the sequence? If so, that would appear to follow directly from the definition of "lim inf" as the infimum of the set of all subsequential limits.

    You then refer to the "bounded series y= sin(x)" which is neither a series nor a sequence but a function.
     
  4. Dec 11, 2008 #3
    so the lim inf is the infimum of the limits of all the sub sequences

    can you give a visual example that shows that

    lim inf Xn<=lim Xn by that lim inf definition

    i cant link them together

    ??
     
    Last edited: Dec 11, 2008
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