Proving |Nk-{x}|=|Nk-1| for the pigeonhole principle

[psycho2499]

Homework Statement

Prove the pigeonhole principle directly. so basically |N_k-{x}|=|N_k-1| if k>1 is an integer and x belongs to the set of naturals.

Homework Equations

The Attempt at a Solution

I have no idea even where to begin.

 

[CompuChip]

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

 

[psycho2499]

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