Results 1 to 2 of 2

Math Help - sets

  1. #1
    Super Member
    Joined
    Aug 2009
    Posts
    639

    sets

    can someone explain to me what the below means?

    consider the set S= (a,b). here b= sup S. let ε > 0, find x ∈ S such that b-ε ≤ a.

    to solve this, there are two cases
    case 1:
    ε≥ b-a. then b-ε≤ a and thus we can take any x of the interval (a,b).

    case 2:
    ε ≤ b-a then b- ε ∈ (a,b). we can take for x to be the midpt of (b-ε, b). clearly, x ∈ (a,b) and b-ε < x.

    can someone explain to me what does the cases talk about becos i have no idea why it works..

    thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello alexandrabel90
    Quote Originally Posted by alexandrabel90 View Post
    can someone explain to me what the below means?

    consider the set S= (a,b). here b= sup S. let ε > 0, find x ∈ S such that b-ε ≤ a. I think this should be b-ε ≤ x.

    to solve this, there are two cases
    case 1:
    ε≥ b-a. then b-ε≤ a and thus we can take any x of the interval (a,b).

    case 2:
    ε ≤ b-a then b- ε ∈ (a,b). we can take for x to be the midpt of (b-ε, b). clearly, x ∈ (a,b) and b-ε < x.

    can someone explain to me what does the cases talk about becos i have no idea why it works..

    thanks!
    Study the diagram I've attached. I hope this will explain what's going on here. In each case you need to explain how to find a number, x, for which b - \epsilon \le x.

    Grandad
    Attached Thumbnails Attached Thumbnails sets-untitled.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Open sets and sets of interior points
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: August 9th 2011, 04:10 AM
  2. Metric spaces, open sets, and closed sets
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: March 16th 2011, 06:17 PM
  3. Replies: 9
    Last Post: November 6th 2010, 01:47 PM
  4. Approximation of borel sets from the top with closed sets.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 18th 2010, 09:51 AM
  5. how to show these sets are 95% confidence sets
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 11th 2009, 10:08 PM

Search Tags


/mathhelpforum @mathhelpforum