Results 1 to 3 of 3

Math Help - Subsequences

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    225

    Subsequences

    Give an example of a sequence that has subsequences converging to every real number
    in [0; 1] and no other real numbers.

    I am confused about subsequences. If I created a sequence that simply listed decimal expansions like this:
    0, 1, .1, .2, .3..., .9, .01, .02, ....09,...
    would that be sufficient?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32

    Re: Subsequences

    Yes, it works. Maybe you should give a formal argument.
    An other example is given by the sequence \left\{|\sin n|\right\}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2008
    Posts
    225

    Re: Subsequences

    Ahh. That's much nicer. Thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Subsequences
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: June 28th 2011, 05:41 PM
  2. Subsequences
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 17th 2010, 07:59 PM
  3. subsequences
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: January 14th 2010, 02:05 AM
  4. Subsequences
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 15th 2009, 11:55 AM
  5. [SOLVED] Subsequences help, please!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 13th 2007, 12:35 PM

Search Tags


/mathhelpforum @mathhelpforum