Results 1 to 2 of 2

Math Help - Is every strictly locally monotone sequence strictly monotone?

  1. #1
    Newbie
    Joined
    Sep 2007
    Posts
    5

    Is every strictly locally monotone sequence strictly monotone?

    Sequence a_n, n=1,2,3... is strictly locally monotone if for every integer k>1 either a_{k-1}< a_k < a_{k+1} OR a_{k-1}> a_k > a_{k+1}.
    Prove every strictly locally monotone sequence is strictly monotone or give counterexample.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by outlandish View Post
    Sequence a_n, n=1,2,3... is strictly locally monotone if for every integer k>1 either a_{k-1}< a_k < a_{k+1} OR a_{k-1}> a_k > a_{k+1}.
    Prove every strictly locally monotone sequence is strictly monotone or give counterexample.
    We know for k=2 we have a_1 < a_2 < a_3 (without lose of generality). We also know for k=3 we have a_2 < a_3 < a_4 or a_2 > a_3 >a_4. It cannot be the latter for a_1 < a_2 < a_3. Thus, a_2<a_3<a_4. So far we know, a_1 < a_2 < a_3 < a_4. Continue this argument.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: May 15th 2011, 03:13 AM
  2. Monotone sequence
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: February 8th 2011, 10:37 AM
  3. Set, monotone sequence, inf
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 17th 2010, 01:52 PM
  4. monotone sequence
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 26th 2009, 08:21 AM
  5. Show strictly monotone
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 11th 2007, 08:37 AM

Search Tags


/mathhelpforum @mathhelpforum