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Thread: Real Analysis: Union of Countable Infinite Sets Proof

  1. September 14th 2010, 10:03 AM #1
    Phyxius117
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    Real Analysis: Union of Countable Infinite Sets Proof

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

    Thanks!!

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  2. September 14th 2010, 10:08 AM #2
    TheEmptySet
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    Behold, the power of SARDINES!
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    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}
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  3. September 14th 2010, 03:23 PM #3
    Phyxius117
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    Would i do this with direct proof or contradiction?
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  4. September 14th 2010, 05:06 PM #4
    Defunkt
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    The method TES offered gives you a direct proof.
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  5. September 14th 2010, 05:38 PM #5
    Phyxius117
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    Thanks!
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« Bijection from [1, infinity) to R | Show a set is countable »

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