# Homework Help: Prove is countable

1. Sep 17, 2010

### The Captain

1. The problem statement, all variables and given/known data
Prove that $$\mathbb Z^{+} X \: \mathbb Z^{+} X \: \mathbb Z^{+}$$ is countable, where X is the Cartesian product.

2. Relevant equations

3. The attempt at a solution
I'm lost as to where to start proving this.

2. Sep 17, 2010

### annoymage

do you know how to prove this

$$\mathbb Z^{+} X \: \mathbb Z^{+}$$

is countable?

3. Sep 17, 2010

### ╔(σ_σ)╝

There are many ways to do this you show that there it bijection from N to ZxZ ,that is , ZxZ is countable. Then show that there is bijection from ZxZ to ZxZxZ.

EDIT
someone beat me to it.

4. Sep 17, 2010

### The Captain

I had to prove that $$\mathbb Z^{+} \: X \: Z^{+} \: \rightarrow \: Z^{+}$$ was one-one and onto using $$f(a,b)=2^{a-1}(2b-1)$$, does that count for proving it's countable, and if it's not, no I don't know how to prove it's countable.

The class I'm taking is a giant leap from Calc 4, and Abstract Algebra isn't even pre-req though it probably should be because the professor keeps asking who's taking it before.

5. Sep 17, 2010

### ╔(σ_σ)╝

Yes, that is a bijection. So you have already shown the first part all you need to do provide a bijection from ZxZxZ to ZxZ .