Let’s start with finite sets, and in reverse: given the two sets A and B, define set C = {a + b | a ∈ a, b ∈ B} For example if A = {1, 3, 7} and B =

Let’s start with finite sets, and in reverse: given the two sets A and B, define set C = {a + b | a ∈ a, b ∈ B} For example if A = {1, 3, 7} and B = {1, 4, 8} , we have C = {1 + 1, 1 + 4, 1 + 8, 3 + 1, 3 + 4, 3 + 8, 7 + 1, 7 + 4, 7 + 8} = {2, 5, 9, 4, 7, 11, 8, 11, 15} = {2, 4, 5, 7, 8, 9, 11, 15} That’s easy. Now, if you didn’t know that, but were given set C, can you find two sets A and B of size 3 that would produce C under that logic? An easy (but cumbersome) way to answer that is: produce all sets of 3 positive integers less than the largest number in C (15 in the example), compute the respective C’s and check whether that’s equal to the targeted C. This problem is about targeting infinite sets of integers for A, B, and C, with an extra twist: for what infinite sets of integers C can you find matching infinitely sized sets A and B that both are subsets of C? Since all of these sets are infinite, the easy but cumbersome method won’t work; neither set has a largest element. In addition, the result isn’t about a specific set of integers.