  A finite set of integers $A$ is a sum-dominant (also called an More Sums Than
Differences or MSTD) set if $|A+A| > |A-A|$. While almost all subsets of $\{0,
\dots, n\}$ are not sum-dominant, interestingly a small positive percentage
are. We explore sufficient conditions on infinite sets of positive integers
such that there are either no sum-dominant subsets, at most finitely many
sum-dominant subsets, or infinitely many sum-dominant subsets. In particular,
we prove no subset of the Fibonacci numbers is a sum-dominant set, establish
conditions such that solutions to a recurrence relation have only finitely many
sum-dominant subsets, and show there are infinitely many sum-dominant subsets
of the primes.
