Results 1 to 3 of 3

Math Help - supremum difference question..

  1. #1
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    supremum difference question..

    f_n(x)=1,1\leq x\leq n\\
    f_n(x)=0,1< n< \infty
    f_n converges to f which is 1
    at the beggining f_n is 0 but when n goes to infinity its 1

    so why sup(f_n(x)-f(x))=1 ?

    f is allways 1

    but f_n is 0 and going to one

    so the supremumum of their difference is 0 not 1

    ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Sampras's Avatar
    Joined
    May 2009
    Posts
    301
    Quote Originally Posted by transgalactic View Post
    f_n(x)=1,1\leq x\leq n\\
    f_n(x)=0,1< n< \infty
    f_n converges to f which is 1
    at the beggining f_n is 0 but when n goes to infinity its 1

    so why sup(f_n(x)-f(x))=1 ?

    f is allways 1

    but f_n is 0 and going to one

    so the supremumum of their difference is 0 not 1

    ?
    you are taking the supremum of the difference. Not just  f_{n}(x) . So you are looking for the least upper bound of the differences.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401
    exacty
    in one case its 1-1
    in the other its 0-1

    the supremum is 0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. supremum proof question
    Posted in the Calculus Forum
    Replies: 8
    Last Post: August 4th 2011, 11:27 AM
  2. Supremum Question
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: January 31st 2010, 05:43 PM
  3. Simple supremum question
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 29th 2009, 01:57 PM
  4. Supremum Question
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 6th 2008, 04:20 PM
  5. infinium and supremum question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 20th 2008, 08:56 AM

Search Tags


/mathhelpforum @mathhelpforum