I am taking a course in computability and logic at my university and am reading about countable and uncountable infinites.
According to my book the set (N X N X N X N...) - where N is a natural number - any finite number of times is countable. I can see how you can reach this conclusion, so that is not my problem.
However what happens if the set (N X N X N ... ) have infinitely many dimensions? Then it becomes uncountable I would say, as you can make a diagonalization argument, but just want to make sure, I have understood it properly.
Many thanks in advance for your help.