Results 1 to 3 of 3

Math Help - why is the intersection of these sets empty?

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    55

    why is the intersection of these sets empty?

    let A_n = [n, infinity)

    why is

    empty?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,386
    Thanks
    1476
    Awards
    1
    Quote Originally Posted by minivan15 View Post
    let A_n = [n, infinity) why is
    empty?
    Given any r>0 there is a positive integer K such that K>r.
    Is this true r\notin A_K?
    So?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by minivan15 View Post
    let A_n = [n, infinity)

    why is

    empty?
    Another way of thinking about is that \left[\bigcap_{n\in\mathbb{N}}A_n\right]'=\bigcup_{n\in\mathbb{N}}A_n'=\bigcup_{n\in\mathb  b{N}}(-\infty,n). Now I surely hope that you recognize that this is \mathbb{R}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. some play on empty sets
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: January 3rd 2012, 08:26 AM
  2. 0 and empty sets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 14th 2011, 06:47 AM
  3. Replies: 5
    Last Post: November 13th 2011, 11:41 AM
  4. empty set and intersection
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: October 4th 2011, 09:54 AM
  5. Proof: Intersection of infinitly many subsets empty?
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: September 17th 2010, 02:50 AM

Search Tags


/mathhelpforum @mathhelpforum