Results 1 to 5 of 5

Math Help - Monotone

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    60

    Monotone

    Is the function z=max(x,2y) monotone? I suppose it is monotone but not strictly montone, isn't it? Sry for posting this rather trivial question, but in our book the max function is described as not monotone, which seems rather weird to me.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: Monotone

    Quote Originally Posted by Schdero View Post
    Is the function z=max(x,2y) monotone?
    What definition of monotone (or monotic) are you using for a function f:\mathbb{R}^2\to \mathbb{R} ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2010
    Posts
    60

    Re: Monotone

    Quote Originally Posted by FernandoRevilla View Post
    What definition of monotone (or monotic) are you using for a function f:\mathbb{R}^2\to \mathbb{R} ?
    Are there various definitions? I thought if f(x)''>0 f(x) is strictly monotone, if f(x)''>=0 it is monotone (in both cases monotonely increasing to be exact). What alternative definition is widely accepted? My example is in a book on econometrics. The question is, whether or not the indifference curves of the utility u=max(x,2y) represent monotone preferences.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: Monotone

    Quote Originally Posted by Schdero View Post
    Are there various definitions?
    Look here:

    Monotonic function - Wikipedia, the free encyclopedia


    My example is in a book on econometrics. The question is, whether or not the indifference curves of the utility u=max(x,2y) represent monotone preferences
    I'm sorry, in that case I'm afraid I can't help you. Perhaps another member, let's wait.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,373
    Thanks
    1315

    Re: Monotone

    Quote Originally Posted by Schdero View Post
    Are there various definitions? I thought if f(x)''>0 f(x) is strictly monotone, if f(x)''>=0 it is monotone (in both cases monotonely increasing to be exact). What alternative definition is widely accepted? My example is in a book on econometrics. The question is, whether or not the indifference curves of the utility u=max(x,2y) represent monotone preferences.
    What you give, f''> 0, is not a definition but as property. A function is strictly monotone increasing if and only if whenever x< y, f(x)< f(y). But that requires an order on the argument of the function. And there is no standard order in two dimensions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: May 15th 2011, 02:13 AM
  2. monotone increasing
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: October 19th 2009, 09:04 AM
  3. monotone sequence
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 26th 2009, 07:21 AM
  4. monotone
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 25th 2008, 10:17 PM
  5. Replies: 1
    Last Post: September 26th 2007, 10:01 AM

Search Tags


/mathhelpforum @mathhelpforum