Is the cardinality of the Cartesian product of two equinumerous infinite sets the same as the cardinality of any one of the sets? I couldn’t find this explicitly stated in any handout or text.
This certainly seems to be true from the examples I have seen:
- The Cartesian product of two infinitely countable sets is again infinitely countable.
- The Cartesian product of two sets with cardinality of continuum again has cardinality of continuum.
I found a question here, but it is with regard to finite sets only.