Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Putnam 1984 B3

  1. Jul 27, 2007 #1
    1. The problem statement, all variables and given/known data
    Isn't the solution at the site http://www.kalva.demon.co.uk/putnam/psoln/psol849.html incomplete because the author assumes he can map the set to Z and we were not given that the set was countably finite? The well-ordering theorem (that states any set can be well-ordered) does not allow you to add indices like that to the set, right?


    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Jul 27, 2007
  2. jcsd
  3. Jul 27, 2007 #2
    Where does he map the set to Z? He's given a set with n elements, hence a finite set, so what he does is perfectly well justified.
     
  4. Jul 27, 2007 #3
    You're right. However, if you were not given that the set were finite or even countable infinite, would you still be allowed to use indices like that? Using the indices i is basically an injection from your set to Z, right?
     
  5. Jul 27, 2007 #4

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    If you well-order the set, then I believe you can pull this off using transfinite recursion.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook