# Math Help - Real Analysis: Union of Countable Infinite Sets Proof

1. ## Real Analysis: Union of Countable Infinite Sets Proof

Here is the problem. How would I go about proving this one?

Thanks!!

2. Consider the function

$\displaystyle f: U \cup V \to \mathbb{N}$ by

$f(z)=\begin{cases}2n-1 \text{ if } z=x_n \\ 2n \text{ if } z=y_n\end{cases}$

3. Would i do this with direct proof or contradiction?

4. The method TES offered gives you a direct proof.

5. Thanks!