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Math Help - Show the set of rational numbers Q is neither open nor closed.

  1. #1
    Junior Member mremwo's Avatar
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    Show the set of rational numbers Q is neither open nor closed.

    How would I show that the set of rational numbers Q is neither closed nor open? Like which theorems would I use? I have been trying this for hours now and can't seem to get anywhere. thanks for your help

    ps- we havent learned the definition of a ball, so please stick to the other more basic definitions
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  2. #2
    Senior Member
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    You can use the fact that both the irrationals and rationals are dense in the reals.

    When working in the reals, a ball is just an interval - I assume you can use intervals?
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