# Proove countability

1. Sep 27, 2013

### aaaa202

1. The problem statement, all variables and given/known data
Proove that Nx{0} is countable. x stand for a product i.e. like the cartesian product NxN

2. Relevant equations
N is countable.

3. The attempt at a solution
This is so obvious since Nx{0} is just (1,0),(2,0) etc. But how do you write a proof formally?

2. Sep 27, 2013

### Dick

Show there is a 1-1 correspondence between Nx{0} and N. Write an explicit bijection. Yes, it is easy.

3. Sep 27, 2013

### aaaa202

So I can define the map:
f: N->Nx{0}
f(x)=(x,0)
and state that this is clearly bijective as a proof?

4. Sep 27, 2013

### jbunniii

I suggest writing the extra few lines to prove injectivity and surjectivity instead of writing "clearly." The problem statement itself seems so obvious that it's tempting to write "clearly" as a one-word proof, but clearly that isn't the intent.