# Proving the pigeonhole directly. I'm stuck.

1. May 5, 2009

### psycho2499

1. The problem statement, all variables and given/known data
Prove the pigeonhole principle directly. so basically |Nk-{x}|=|Nk-1| if k>1 is an integer and x belongs to the set of naturals.

2. Relevant equations

3. The attempt at a solution
I have no idea even where to begin.

2. May 6, 2009

### CompuChip

Doesn't it suffice to write down a bijection between the two sets you mentioned?

3. May 7, 2009

### psycho2499

Yeah I guess that would work since things are equivalent if they are a bijection. Thanks man