On the last handson in morphology we were considering cross products of languages and their regexes, for example: A = {a} and B = {b}
(A+ cross product B+) gives us sequences: ab, aab, aaab, abb, abbb, aabb and so on
we defined as well that:
(A cross product B) + gives us only pairs of same length ab, aabb, aaabbb and so on.
Intuitively it doesn't seem right if we first create a cross product which in this case is "ab" and then apply + we would expect sequences ab,abab, ababab and so on. How to interpret or how to think about it, that + of cross product outputs only same length sequences?