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Math Help - prove it!!!

  1. #1
    Member
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    Aug 2008
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    prove it!!!

     \bigcup _ { n=1} ^ \infty (1+\frac {1}{n} , 4-\frac{1}{n})= (1,4)
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  2. #2
    Junior Member
    Joined
    Aug 2009
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    Hi.
     x \in \bigcup _ { n=1} ^ \infty (1+\frac {1}{n} , 4-\frac{1}{n}) if and only if \left( \exists n \in  \mathbb{N}\right) x \in (1+\frac {1}{n} , 4-\frac{1}{n}).
    \left( \exists n \in  \mathbb{N}\right) x \in (1+\frac {1}{n} , 4-\frac{1}{n}) if and only if  x \in (1 , 4).

    Can you see why each 'if and only if' holds?
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