Consider 2 sets of numbers $\{a_1,...,a_J\}$ and $\{b_1,...,b_J\}$.
(A1) We know that $a_1<...<a_J$ and $b_1<...<b_J$.
Now consider the $J^2$ differences of each element of the first set with each element of the second set: $$ a_1-b_1\\ a_1-b_2\\ ...\\ a_1-b_J\\ a_2-b_1\\ a_2-b_2\\ ...\\ a_2-b_J\\ ...\\ a_J-b_J $$
Does (A1) allow to order from smallest to largest the differences? If not, does (A1) allow to say which is the biggest and the smallest difference? If not, does (A1) allow to say anything about the ordering of the differences?
(suggestions on more appropriate tags are welcome!)