Results 1 to 3 of 3

Math Help - real number system

  1. #1
    Newbie
    Joined
    Apr 2007
    Posts
    15

    real number system

    I would appreciated if someone knows how to do this:

    If x and y are arbitrary real numbers with x<y, prove that there is at least one z satisfying x < z < y.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by RB06 View Post
    I would appreciated if someone knows how to do this:

    If x and y are arbitrary real numbers with x<y, prove that there is at least one z satisfying x < z < y.

    Thanks
    well, i don't know how rigorous you want to be here, but it seems to me that all we have to do is find a number that satisfies the requirements to be z.

    So, let x and y be arbitrary real numbers such that x < y. then the distance between x and y is given by |y - x|. Take half this distance. thus we have the quantity \frac {|y - x|}2 which is greater than zero

    Clearly we have x < x + \frac {|y - x|}2 < y. thus we can let z = x + \frac {|y - x|}2

    So we have found one z that satisfies the conditions.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    x< \frac{x+y}{2} < y
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Real number system
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 21st 2011, 04:03 PM
  2. Real Number
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 6th 2009, 10:11 PM
  3. Proof , Real system
    Posted in the Calculus Forum
    Replies: 9
    Last Post: January 20th 2008, 01:20 PM
  4. Help with Real Number System?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 14th 2007, 05:07 PM
  5. Real Number System
    Posted in the Algebra Forum
    Replies: 8
    Last Post: February 2nd 2007, 02:47 PM

Search Tags


/mathhelpforum @mathhelpforum