I disagree. You can consider the first or the second index as negligible or as not written. In my opinion the final result must depend in a continuous way on each of the indices. Note, we are calculating the number of elements a_ij. This number does not change when one of the indices becomes smaller and smaller and finally fades away or reappeares.
At least one must confess that the results of set theory cannot be applied to any scientific purpose, although Cantor asserted that he had developed set theory for dealing with physical, chemical and political issues.
