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!

Sequence and subsequence - real analysis

  1. Feb 22, 2015 #1
    Solving last exam and stuck in this exercise
    1. The problem statement, all variables and given/known data
    Consider an increasing sequence {xn} . We suppose ∃ x∈ℝ and {xnk} a sebsequence of {xn} and xnk→x
    a/ Show that for any n∈ℕ , ∃ k∈ℕ as n≤nk
    b/ Show that xn→x
    2. Relevant equations
    3. The attempt at a solution

    For b/ it is easy.
    But for a/ I really don't know how to do that

  2. jcsd
  3. Feb 23, 2015 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    I don't know how to interpret that statement. What is it that happens "as" [itex] n \le n_k [/itex] ?
  4. Feb 23, 2015 #3


    User Avatar
    Science Advisor

    If you mean "n∈ℕ , ∃ k∈ℕ such that n≤nk" that just says that, given any integer n, there exist an "nk", an index from the subsequence, larger than n. And that comes from the fact that the subsequence is infinite.
  5. Feb 23, 2015 #4
    Yes sorry it is such that , it was late !
    I dont know where to start from to get to this result ? :oldconfused:
  6. Feb 25, 2015 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Well, what do you mean by nk ?

    Isn't {nk} an increasing sequence in , so that {xnk} is a subsequence ?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted