Originally Posted by

**ecnanif**

I my book, it says: To prove that a set $\displaystyle A$ is denumerable you should find a bijection $\displaystyle f : \mathbb{N} \to \mathbb{A} $.

Now, I need to prove that $\displaystyle \mathbb{Q} $ is denumerable.

So I replace my $\displaystyle A$ with $\displaystyle \mathbb{Q} $ in the previous paragraph. Now I need to find a bijection $\displaystyle f$.

Would it be equivalent to find a bijection $\displaystyle f: \mathbb{Q} \to \mathbb{N} $ ?

If so, I need to find a function that takes the rational numbers to $\displaystyle \mathbb{N}$. Also, it need to be injective.

It should be suffiecient to find a bijection $\displaystyle f: \mathbb{Q} \to G \subseteq \mathbb{N} $ ?

What could $\displaystyle f$ look like?