# Infinite Union of Uncountable Sets (quick ques)

1. 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
2. Mar 26, 2009

### CompuChip

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

3. 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.