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Math Help - countable and uncountable sets

  1. #1
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    countable and uncountable sets

    Hi Im studying for my final and have always been uneasy about countable and uncountable sets. I know the reals are uncountable but what about subsets of the reals, ie is (1,2) countable? (0,5)? etc..

    Thanks
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  2. #2
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    Quote Originally Posted by scubasteve123 View Post
    Hi Im studying for my final and have always been uneasy about countable and uncountable sets. I know the reals are uncountable but what about subsets of the reals, ie is (1,2) countable? (0,5)? etc..

    Thanks

    Every non-trivial interval of the reals is uncountable. Googe "Cantor's Diagonal Proof". That's usually done for the interval (0,1) but it's easy to generalize to any interval.

    Tonio
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