Results 1 to 4 of 4

Math Help - absolute value continuity

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    31

    absolute value continuity

    It is very easy to prove that abs(x) is continuous everywhere using epsilon-delta techniques. Yet, let U = (0,1). This is open in [0, infinity). Yet, f inverse (U) can be said to equal (0,1) U {-1/2} right? This set, call it V is certainly not open in (- infinity, infinity).

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1

    Re: absolute value continuity

    Quote Originally Posted by grandunification View Post
    It is very easy to prove that abs(x) is continuous everywhere using epsilon-delta techniques. Yet, let U = (0,1). This is open in [0, infinity). Yet, f inverse (U) can be said to equal (0,1) U {-1/2} right? This set, call it V is certainly not open in (- infinity, infinity).
    What?
    f^{-1}(U)=(-1,0)\cup(0,1) which is open.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2009
    Posts
    31

    Re: absolute value continuity

    Quote Originally Posted by Plato View Post
    What?
    f^{-1}(U)=(-1,0)\cup(0,1) which is open.
    The preimages aren't unique. One preimage would be the union of (0,1) with the singleton set {-1/2}. f((0,1)) = (0,1) and f({-1/2}) = 1/2 which is an element of (0/1).
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Feb 2009
    Posts
    31

    Re: absolute value continuity

    Disregard that comment above. I was not really using the proper definition of a preimage. I have to consider ALL elements which map onto the image. Thank-you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Absolute continuity
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: December 4th 2011, 08:58 AM
  2. Replies: 2
    Last Post: February 5th 2011, 11:54 PM
  3. Replies: 8
    Last Post: May 23rd 2010, 11:59 PM
  4. Analysis: Absolute Continuity & Differentiation
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 22nd 2010, 05:50 AM
  5. Absolute Continuity
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 20th 2008, 11:54 AM

Search Tags


/mathhelpforum @mathhelpforum