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Math Help - uncountability

  1. #1
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    uncountability

    We want to prove that  [a,b] and  (a,b) are uncountable.

    The book says that there are bijections from  (a,b) onto  (-1,1) onto unit semicircle. From this point how do we deduce that  (a,b) is uncountable?

     [a,b] is then uncountable if we prove that  (a,b) is uncountable.
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  2. #2
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    Quote Originally Posted by shilz222 View Post
    We want to prove that  [a,b] and  (a,b) are uncountable.

    The book says that there are bijections from  (a,b) onto  (-1,1) onto unit semicircle. From this point how do we deduce that  (a,b) is uncountable?

     [a,b] is then uncountable if we prove that  (a,b) is uncountable.
    The diagnol argument shows that (0,1) is uncountable. That that means (-1,1) is uncountable because it contains it as a subset.
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