Results 1 to 2 of 2

Math Help - Inf A= 0 <=> 0 is an accumulation point

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    23

    Inf A= 0 <=> 0 is an accumulation point

    Let A be a subset of the positive real. Prove that inf a = 0 <=> 0 is accmulation point of A

    is it still true if A is the set of non negative reals? proof or give counter example

    So I think I understand why this is true...since inf A=0 A is bounded below by 0, and we can have elements of A as close as we want to 0, but I dont know how to write it out?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by mtlchris View Post
    Let A be a subset of the positive real. Prove that inf a = 0 <=> 0 is accmulation point of A
    is it still true if A is the set of non negative reals? proof or give counter example
    Notice that if c>0 then c is not a lower bound for A.
    So \left( {\exists x \in A} \right)\left[ {0 < x < c} \right].
    In this way construct a decreasing sequence of distinct terms from A converging to 0.

    Consider this set of nonnegative numbers: \left\{ 0 \right\} \cup \left\{ {  2 + \frac{1}{n}:n \in \mathbb{Z}^ +  } \right\}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. accumulation point
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: April 29th 2011, 09:03 AM
  2. accumulation point help
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: February 4th 2010, 11:30 AM
  3. Accumulation point
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: January 27th 2010, 04:43 PM
  4. accumulation point
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 19th 2009, 02:11 PM
  5. Accumulation Point
    Posted in the Calculus Forum
    Replies: 7
    Last Post: August 19th 2007, 01:53 AM

Search Tags


/mathhelpforum @mathhelpforum