Can we only have a Cartesian product of a countable number of sets?
I suspect the answer to this is yes. This is because the resulting tuple of the Cartesian product will be ordered, and each position on that tuple will have a number- as a mark of position. This number will undoubtedly be a natural numbers. This number (position) can also be given to the set from which the element at that position is taken, hence making the number of sets countable.
I'm not sure of the above explanation. Verification would be extremely helpful. Thanks