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Abstract Function

  1. Aug 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Function f(x) defined in [0,1],and f(0)=f(1).If [tex]x_{1},x_{2}\in[0,1][/tex] then [tex]|f(x_{1})-f(x_{2})|<|x_{1}-x_{2}|[/tex] (*)
    Prove [tex]|f(x_{1})-f(x_{2})|<1/2[/tex]


    2. Relevant equations
    I think maybe |a|-|b|[tex]\leq[/tex]|a-b|[tex]\leq[/tex]|a|+|b| will be helpful


    3. The attempt at a solution
    Well,I get some information from (*),I can prove that f(x)+x is monotone increasing and f(x)-x is monotone decreasing.Then I don't know what I should do. And I'm not sure whether I'm in the right way.

    PS: why I can't see LaTex images clearly.They appear to be a black background and letters numbers or signs are not easy to recognize
     
    Last edited: Aug 15, 2009
  2. jcsd
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