Results 1 to 4 of 4

Math Help - Finding the supremum and/or infimum of these sets.. (real analysis)

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    Surrey
    Posts
    19

    Finding the supremum and/or infimum of these sets.. (real analysis)

    I've been working on real analysis for a short time and am really struggling to find the supremum and infimum of these sets (or if they exist at all)

    the set of rational numbers in the interval [0,1]

    the set of real numbers in the half open interval ]0,1]

    the half line x ∈ R | x≤0

    S={(x^2+y^2/xy)|x>0, y>0}

    thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1

    Re: Finding the supremum and/or infimum of these sets.. (real analysis)

    Quote Originally Posted by kaya2345 View Post
    I've been working on real analysis for a short time and am really struggling to find the supremum and infimum of these sets (or if they exist at all)
    the set of rational numbers in the interval [0,1]
    the set of real numbers in the half open interval ]0,1]

    the half line x ∈ R | x≤0

    S={(x^2+y^2/xy)|x>0, y>0}
    The first two have both inf & sup. And they are the same for both set.

    The third has only sup.

    For the fourth, is that the same as \frac{x}{y}+\frac{y}{x}~?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2012
    From
    Surrey
    Posts
    19

    Re: Finding the supremum and/or infimum of these sets.. (real analysis)

    Quote Originally Posted by Plato View Post
    The first two have both inf & sup. And they are the same for both set.

    The third has only sup.

    For the fourth, is that the same as \frac{x}{y}+\frac{y}{x}~?
    thank you for that do the first two have both because they're rational and real? would it not be different for the half open interval?

    and yes the fourth is the same as x/y + y/x
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1

    Re: Finding the supremum and/or infimum of these sets.. (real analysis)

    Quote Originally Posted by kaya2345 View Post
    thank you for that do the first two have both because they're rational and real? would it not be different for the half open interval?

    and yes the fourth is the same as x/y + y/x


    NO. \inf(0,1]=0~\&~\inf[0,1]=0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 23rd 2012, 08:11 AM
  2. analysis : infimum/supremum proof
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: February 23rd 2009, 07:19 PM
  3. Real Analysis-Supremum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 27th 2009, 08:45 PM
  4. Supremum Question for real analysis
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 6th 2008, 02:33 PM
  5. real analysis supremum question
    Posted in the Calculus Forum
    Replies: 15
    Last Post: September 23rd 2007, 06:34 PM

Search Tags


/mathhelpforum @mathhelpforum