Results 1 to 2 of 2

Math Help - Accumulation points, dense set

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    8

    Accumulation points, dense set

    Let S be contained in \mathbb{R} and let A be the set of accumulation points of S. Prove S is dense in <br />
\mathbb{R} iff. A= <br />
\mathbb{R}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Focus's Avatar
    Joined
    Aug 2009
    Posts
    228
    Quote Originally Posted by pirouette View Post
    Let S be contained in \mathbb{R} and let A be the set of accumulation points of S. Prove S is dense in <br />
\mathbb{R} iff. A= <br />
\mathbb{R}
    What is your definition of dense? Is it that for each ball in the reals, it contains a point of S?

    If so then suppose that S is dense. Let x \in \mathbb{R}, then for each open set around x, it contains an element of S. Hence x \in A. As x was arbitrary, we have that A=\mathbb{R}.

    Similarly the other way round.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. accumulation points or limits points
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 27th 2010, 03:20 AM
  2. About accumulation points..
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: October 24th 2010, 06:28 AM
  3. accumulation points
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: September 25th 2010, 09:44 AM
  4. Replies: 3
    Last Post: January 11th 2009, 12:49 PM
  5. Accumulation Points
    Posted in the Calculus Forum
    Replies: 0
    Last Post: December 20th 2008, 07:28 PM

Search Tags


/mathhelpforum @mathhelpforum