Infinite Union of Uncountable Sets (quick ques)

Thread starter logarithmic
Start date Mar 26, 2009
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Infinite Sets Union

Mar 26, 2009

logarithmic

Is the infinite union of uncountable sets also uncountable? Just need a yes or no. Thanks.

Last edited: Mar 26, 2009

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Mar 26, 2009

CompuChip

Science Advisor

Homework Helper

Any interval in the reals is uncountable. So even a finite union of uncountable sets is uncountable.

Mar 26, 2009

AUMathTutor

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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