Is a Subset of a Countable Set also Countable?

[kirschplunder]

Homework Statement

I got to proof that the statement is denumberable

Homework Equations

The Attempt at a Solution

My attempt was that 2^k != 3^k (is not) for all k in N (natural numbers)

 

[JG89]

The set is obviously infinite. So now all you have to do is prove that a subset of a countable set is also countable.

I think proving this in general will be easier than attacking the specific question you posted.