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

Trying to understand lim sup

  1. Feb 25, 2012 #1
    Suppose there is some sequence [itex] \{x_n\}_{n\in\mathbb{N}}[/itex]. Say we have a set of all the limits of all possible subsequences, would the supremum of this set be the superior limit of [itex] \{x_n\}_{n\in\mathbb{N}}[/itex]? What about if this value turns out to be 5, but there is a member of the sequence that is equal to 500, but is not the limit of any subsequence. Can the superior limit be lower than the supremum of the sequence? Thanks!
  2. jcsd
  3. Feb 27, 2012 #2


    User Avatar
    Science Advisor

    limsup may be lower than sup. Example xn = 1 + 1/n, sup = 2, limsup = 1.
  4. Feb 27, 2012 #3
    Thanks, that was quite helpful.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook