Results 1 to 2 of 2

Math Help - infimums and supremums

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    19

    infimums and supremums

    Find and Prove the inf and sup:

    {x is a rational number: x^2 < 2 }
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2009
    From
    United Kingdom
    Posts
    9
    If you were taking x in the real numbers, then your supremum would be \sqrt 2 and your infimum would be  - \sqrt 2 .

    However, these are both irrational numbers. There does not exist a supremum (least upper bound) in the rational numbers. Say it did exist, and call it a. Then {a^2} > 2. Define b = \frac{{2a + 2}}{{a + 2}}. Then b is also an upper bound of your set, and b < a, which contradicts our assumption that a was our LEAST upper bound.

    A similar argument works for the infimum.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. metric spaces and infimums
    Posted in the Differential Geometry Forum
    Replies: 10
    Last Post: November 13th 2010, 06:16 PM
  2. infimums and supremums of Functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 19th 2009, 06:06 AM
  3. inequality of supremums
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 27th 2009, 01:32 AM
  4. infimum and supremums
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 16th 2008, 04:07 AM
  5. Replies: 3
    Last Post: January 15th 2008, 11:46 PM

Search Tags


/mathhelpforum @mathhelpforum