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..
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.