1. Not finding help here? Sign up for a free 30min 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!

Real Analysis: bunch of true and false questions

  1. Nov 14, 2008 #1
    Problem Statements

    a. if a sequence is montone then every one of its subsequences is monotone.

    true.

    b. if a sequence is not monotone, then every one of its subsequences is not monotone

    false.

    c. if a sequence is unbounded, then every one of its susequences is unbounded.

    true

    d. if a sequene is divergent, then it cannot have a convergent subsequence

    false

    e. if a sequence tends to +inf, then it cannot have a convergent subsequence

    true

    f. if a sequence is unbounded, then it cannot have a convergent subsequence

    false

    g. if lim sup s_n = 0, then lim sup|s_n| = 0


    false

    h. if kim sup|s_n| = 0, then lim sup s_n = 0

    true

    i. if lim sup|s_n| = 5, then lim sup s_n = 5

    true

    j. if lim sup|s_n|= 5, then (s_n) is bounded

    false


    I actually have to prove out the ones that are true but can someone just let me know if I got the first step right on them. Thanks alot!!
     
  2. jcsd
  3. Nov 14, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What about the sequence 1, 2, 3, 2, 4, 2, 5, 2, 6, 2, ... ?

    What about the sequence 1, 2, 3, 2, 4, 2, 5, 2, 6, 2, ... ?

    What about the sequence -5, -5, -5, ... ?

     
  4. Nov 14, 2008 #3
    thanks so much! those are some attractive sequences.
     
  5. Nov 14, 2008 #4

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    (e) looks true to me... halls, your counterexample doesn't tend to +infinity
     
  6. Nov 14, 2008 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, thanks, Office Shredder, I was thinking of an unbounded sequence.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Real Analysis: bunch of true and false questions
  1. True or False Analysis (Replies: 15)

  2. True/false questions (Replies: 4)

Loading...