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Thread: why is the intersection of these sets empty?

  1. #1
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    why is the intersection of these sets empty?

    let A_n = [n, infinity)

    why is

    empty?
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  2. #2
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    Quote Originally Posted by minivan15 View Post
    let A_n = [n, infinity) why is
    empty?
    Given any $\displaystyle r>0$ there is a positive integer $\displaystyle K$ such that $\displaystyle K>r$.
    Is this true $\displaystyle r\notin A_K?$
    So?
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by minivan15 View Post
    let A_n = [n, infinity)

    why is

    empty?
    Another way of thinking about is that $\displaystyle \left[\bigcap_{n\in\mathbb{N}}A_n\right]'=\bigcup_{n\in\mathbb{N}}A_n'=\bigcup_{n\in\mathb b{N}}(-\infty,n)$. Now I surely hope that you recognize that this is $\displaystyle \mathbb{R}$.
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