# Proove countability

## Homework Statement

Proove that Nx{0} is countable. x stand for a product i.e. like the cartesian product NxN

N is countable.

## 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?

Dick
Homework Helper

## Homework Statement

Proove that Nx{0} is countable. x stand for a product i.e. like the cartesian product NxN

N is countable.

## 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?

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

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

jbunniii