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

Thanks!!

http://i10.photobucket.com/albums/a1.../problem32.png

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- Sep 14th 2010, 10:03 AMPhyxius117Real 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 AMTheEmptySet
Consider the function

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

$\displaystyle f(z)=\begin{cases}2n-1 \text{ if } z=x_n \\ 2n \text{ if } z=y_n\end{cases}$ - Sep 14th 2010, 03:23 PMPhyxius117
Would i do this with direct proof or contradiction?

- Sep 14th 2010, 05:06 PMDefunkt
The method TES offered gives you a direct proof.

- Sep 14th 2010, 05:38 PMPhyxius117
Thanks!