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Constructing Bijections

  1. Sep 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Let w,x,y,z be real #'s with w<x and y<z

    Construct bijections
    [w,x] <-> [y,z]
    (w,x] <-> [y,z)

    2. Relevant equations

    3. The attempt at a solution

    So for the closed interval bijection, I was trying to work with the following:

    (z-y)/(x-w) * (f-w) + y where w,x,y,z are the #'s and f is the function variable.

    If I'm not mistaken, this is injective and surjective, thus bijective.

    One thing I was wondering is simply what it means to "construct" the bijection?? Does it just mean presenting the equation above and showing that it is 1-1 and onto? Or is there something more complex at work?

    And for the (...] <-> [...) portion, I am at a loss. Can this be done in a regular function type format, or do I need to do it piecewise?

    Thanks
    Pete
     
  2. jcsd
  3. Sep 14, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Pete! Welcome to PF! :smile:
    Yes, "construct" just means presenting an equation.
    oh come on

    imagine you're a three-year-old child and you're presented with two [) and (] -shaped bricks :rolleyes: :wink:
     
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