# Prove set is countable

1. Sep 4, 2013

### aaaa202

1. The problem statement, all variables and given/known data
Prove that {m+n, m,n $\in$Z} is countable

2. Relevant equations

3. The attempt at a solution I Can prove it if I make a nxn scheme and put 1,-1,2,-2 along each side. This generates a table which when counted a long first,second etc. Diagonal hits all the numsers in the given set. But is this the formal Way to prove these kinds of things?

2. Sep 4, 2013

### johnqwertyful

Isn't that set just equal to Z again? Maybe I'm just misunderstanding notation...

3. Sep 4, 2013

### Staff: Mentor

The set could also be described as {p | p = m + n, where m, n $\in$ Z}. All you need to do is to establish a one-one pairing with the integers. The things in the set are just numbers, not ordered pairs, so based on the notation you've used, your table is way more complicated than what is needed.

That's how I read it as well.