Results 1 to 2 of 2

Thread: Real Numbers Inequality Proof

  1. March 30th 2011, 12:03 AM #1
    jstarks44444
    jstarks44444 is offline
    Member
    Joined
    Nov 2010
    Posts
    86

    Real Numbers Inequality Proof

    Let x,y be elements of the Real Numbers such that x < y. There exists z in the Real Numbers such that x < z < y.

    Any thoughts on this proof?
    Follow Math Help Forum on Facebook and Google+
  2. March 30th 2011, 01:28 AM #2
    FernandoRevilla
    FernandoRevilla is offline
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,154
    Thanks
    38
    Quote Originally Posted by jstarks44444 View Post
    Let x,y be elements of the Real Numbers such that x < y. There exists z in the Real Numbers such that x < z < y.

    Choose z=(1/2)(x+y) and use the standard arithmetic and ordering axioms of \mathbb{R} .
    Follow Math Help Forum on Facebook and Google+
« Least Upper Bound proof | Greatest Lower Bound project »

Similar Math Help Forum Discussions

  1. Quick Proof on real numbers
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: September 15th 2011, 04:05 AM
  2. proof of unaccountability of the real numbers w.r.t the non-uniqueness of decimals
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 26th 2010, 08:27 AM
  3. Proof Dealing with real and rational numbers
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 20th 2010, 08:26 PM
  4. Sequence of real numbers | Proof of convergence
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: January 25th 2010, 02:22 PM
  5. inequality on the set of real numbers
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 31st 2007, 09:04 AM

Search Tags


/mathhelpforum @mathhelpforum