# Putnam 1984 B3

1. Jul 27, 2007

### ehrenfest

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. Jul 27, 2007

### d_leet

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.

3. Jul 27, 2007

### ehrenfest

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?

4. Jul 27, 2007

### morphism

If you well-order the set, then I believe you can pull this off using transfinite recursion.

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