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Infinite Union of Uncountable Sets (quick ques)

  1. Mar 26, 2009 #1
    Is the infinite union of uncountable sets also uncountable? Just need a yes or no. Thanks.
     
    Last edited: Mar 26, 2009
  2. jcsd
  3. Mar 26, 2009 #2

    CompuChip

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    Any interval in the reals is uncountable. So even a finite union of uncountable sets is uncountable.
     
  4. Mar 26, 2009 #3
    Yes, any union of any uncountable set is also uncountable.

    Remember, the union of sets can't be any smaller than the individual set.
     
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