Results 1 to 4 of 4

Math Help - supremum

  1. #1
    Junior Member
    Joined
    Jul 2006
    Posts
    73

    supremum

    For each of these sets for their, supremum and infimum (if they exist), maximum and minimum (if they exist), interior (explain your reasoning), boundary (explain your reasoning), set of accumilation points (explain your reasoning), closure
    and classify each of these sets as open, closed, neither open nor closed, or both open and
    closed.

    a) [3,5)
    b) N --- natural numbers
    c) { x is an element of Q: o <= x <= sqrt(2) } = Q and [0,sqrt(2)]

    the and means the upside down U
    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 luckyc1423 View Post
    For each of these sets for their, supremum and infimum (if they exist), maximum and minimum (if they exist), interior (explain your reasoning), boundary (explain your reasoning), set of accumilation points (explain your reasoning), closure
    and classify each of these sets as open, closed, neither open nor closed, or both open and
    closed.

    a) [3,5)
    b) N --- natural numbers
    c) { x is an element of Q: o <= x <= sqrt(2) } = Q and [0,sqrt(2)]

    the and means the upside down U
    I can only help you with supremum and infimum, maximum and minimum, boundary, and the classifications of open, closed etc.

    I have no idea what "interior" or "closure" means, and i only have a very vague idea of what "accumilaation" means

    a) [3,5)
    Let S be the set [3,5)

    supremum = 5
    infimum = 3
    maximum = doesnt exist
    minimum = 3
    boundary (explain): bounded above and below. Below by 3, since if s is an element of S, then 3<= s for all s in S. Above by 5, since if s is an element of S, 5>= s for all s in S
    classification: Both open and closed. Closed at the lower bound, open at the upper bound

    b) N --- natural numbers

    supremum = doesnt exist (i guess you could say + infinity, dont hold me to this though)
    infimum = 1
    maximum = doesnt exist
    minimum = 1
    boundary (explain): Bounded below by 1. Since if n is an element of N, then 1<= n for all n in N. It is unbounded above
    classification: closed at lower bound open at upper bound

    c) { x is an element of Q: o <= x <= sqrt(2) } = Q and [0,sqrt(2)]

    Let R be the set { x is an element of Q: o <= x <= sqrt(2) }

    supremum = sqrt(2)
    infimum = 0
    maximum = doesnt exist
    minimum = doesnt exist
    boundary (explain): bounded below by 0, since if r is an element of R, 0 <= r for all r in R. bounded above by sqrt(2), since if r is an element of R, sqrt(2) >= r for all r in R
    classification: open

    I guess someone will come along soon who can help you with the other parts
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,403
    Thanks
    1486
    Awards
    1
    The boundary of a set, denoted as Bdry(S) is the set of points that are in the set and limits points of its complement or points in its complement that are limits points of the set.
    Thus Bdry((3,5])={3,5}; Bdry{N}={1} [here be careful some text say that 0 is a natural number!];
    Bdry({ x is an element of Q: o <= x <= sqrt(2) }=[0,sqrt(2)]. That is the whole set is a subset of its own boundary.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jul 2006
    Posts
    73
    Thank you guys, it really helps when you guys explain things..when I go back to look at how everything is done it really helps out having these examples explained from you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. supremum
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: January 15th 2011, 03:54 PM
  2. Supremum
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: January 5th 2011, 04:12 PM
  3. Supremum
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 22nd 2008, 11:29 AM
  4. Supremum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 13th 2008, 07:21 AM
  5. Supremum example
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 29th 2008, 11:22 PM

Search Tags


/mathhelpforum @mathhelpforum