Thread: countable and uncountable sets

Hi Im studying for my final and have always been uneasy about countable and uncountable sets. I know the reals are uncountable but what about subsets of the reals, ie is (1,2) countable? (0,5)? etc..

Thanks

Originally Posted by scubasteve123

Hi Im studying for my final and have always been uneasy about countable and uncountable sets. I know the reals are uncountable but what about subsets of the reals, ie is (1,2) countable? (0,5)? etc..

Thanks

Every non-trivial interval of the reals is uncountable. Googe "Cantor's Diagonal Proof". That's usually done for the interval (0,1) but it's easy to generalize to any interval.

Tonio