Infinite Union of Uncountable Sets (quick ques)

[logarithmic]

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

 

[CompuChip]

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

 

[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.