1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about monotonic sequences.

  1. Mar 13, 2012 #1
    1. The problem statement, all variables and given/known data
    If I have a constant sequence a,a,a,a,a,a, Is that monotonic?
    because I have conflicting definitions some say that it has to increase or decrease,
    but some say it just has to not increase or not decrease.
    And also does every bounded sequence have monotonic sub sequence.

    3. The attempt at a solution
    I think that every bounded sequence has a monotonic sub sequence. Because I would eventually have to have an infinite amount of points that were the same or an infinite amount that were increasing or decreasing.
     
  2. jcsd
  3. Mar 13, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I think most texts allow equality in the definition of monotone sequence and call the sequence "strictly monotone" for the case where strict inequality is used in the definition.

    About your last question, I think so too, but can you prove it? Do you know the Bolzano Weierstrass theorem? It might help you construct an argument.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question about monotonic sequences.
  1. Monotonic sequences (Replies: 21)

  2. Monotonic sequences (Replies: 5)

  3. Monotone sequences (Replies: 1)

Loading...