Results 1 to 2 of 2

Math Help - intersecting intervals

  1. #1
    Newbie
    Joined
    Oct 2006
    Posts
    6

    intersecting intervals

    Question attatched
    Attached Thumbnails Attached Thumbnails intersecting intervals-qc.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,912
    Thanks
    1760
    Awards
    1
    None of the intervals can be unbounded, right or left rays. Otherwise there is a counter-example.
    Name the interval with the least left end point I_1. There are at most six intervals that may share a point with it. So we have at least 43 which have no point common with I_1. Of those, name the interval with the least left end point I_2. Again are at most six intervals that may share a point with I_2, leaving 36 that have no point either of the two named. We continue getting I_3 from 28 and so fourth until we get I_8 from 8.
    Now you have 8 intervals that are pairwise disjoint.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Intersecting Circles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 7th 2011, 05:07 PM
  2. Intersecting lines
    Posted in the Geometry Forum
    Replies: 2
    Last Post: December 18th 2010, 08:47 PM
  3. intervals of increase and the intervals of decrease?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 28th 2010, 10:00 PM
  4. Two circles intersecting each other...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 25th 2010, 11:32 AM
  5. intersecting circles
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: March 14th 2009, 01:22 AM

Search Tags


/mathhelpforum @mathhelpforum