Results 1 to 2 of 2

Math Help - Transformations of a set that can't be non-decreasing under any well-order

  1. #1
    Member
    Joined
    Feb 2011
    Posts
    147
    Thanks
    3

    Transformations of a set that can't be non-decreasing under any well-order

    Let X be a set. Which functions from X to itself cannot be non-decreasing if we equip X with any well-order ≤, the same in X as the domain and X as the codomain?

    Such functions obviously exist. For example, if we take X={0,1} and the function f(x)=~x ("~" denoting negation), then there is no well-order on X making this a non-decreasing function.

    But what are these functions in general? Does a composition of such functions also have this property?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Feb 2011
    Posts
    147
    Thanks
    3

    Re: Transformations of a set that can't be non-decreasing under any well-order

    I've just realized that the last question is not the one I need an answer to. I wanted to ask whether a composition of functions that satisfy the negation of this property also does. That is, if f,g:X\longrightarrow X are functions and there are two well-orders \leq_f,\leq_g on X such that f : (X,\leq_f)\longrightarrow(X,\leq_f) and g : (X,\leq_g)\longrightarrow(X,\leq_g) are both non decreasing, then is there a well-order \leq_{f\circ g} on X such that f\circ g : (X,\leq_{f\circ g})\longrightarrow(X,\leq_{f\circ g}) is non-decreasing?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 2nd order PDE, using transformations...?
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: April 27th 2010, 01:44 PM
  2. Decreasing annuity
    Posted in the Business Math Forum
    Replies: 2
    Last Post: March 14th 2010, 10:23 AM
  3. Increasing/Decreasing and Abs Max and Min
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 28th 2009, 06:57 PM
  4. Decreasing function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 21st 2008, 09:23 AM
  5. Decreasing
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 2nd 2006, 08:27 PM

Search Tags


/mathhelpforum @mathhelpforum