# Real Analysis: Union of Countable Infinite Sets Proof

• Sep 14th 2010, 10:03 AM
Phyxius117
Real Analysis: Union of Countable Infinite Sets Proof
Here is the problem. How would I go about proving this one?

Thanks!!

http://i10.photobucket.com/albums/a1.../problem32.png
• Sep 14th 2010, 10:08 AM
TheEmptySet
Consider the function

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

$f(z)=\begin{cases}2n-1 \text{ if } z=x_n \\ 2n \text{ if } z=y_n\end{cases}$
• Sep 14th 2010, 03:23 PM
Phyxius117
Would i do this with direct proof or contradiction?
• Sep 14th 2010, 05:06 PM
Defunkt
The method TES offered gives you a direct proof.
• Sep 14th 2010, 05:38 PM
Phyxius117
Thanks!