I am interested in the sum set operation on subsets of the integers $\mathbb Z$:
$$A + B = \{ x + y | x \in A, y \in B\}$$
One readily arrives at the following cardinality bounds:
$$|A| + |B| - 1 \leq |A + B| \leq | A |\cdot | B |$$ for $A, B$ non empty and finite
What happens if $B$ is co-finite, i.e complement of $B$ is finite?
Any cardinality bounds of the complement of the set sum known?
Bye