I will present a result in combinatorial number theory due to Renling Jin:  if A and B are subsets of the natural numbers with positive Banach density, then their sum A+B is piecewise syndetic, a robust notion of largeness for subsets of the natural numbers.  The result bears a resemblance to a theorem of real analysis due to Steinhaus:  if C and D are subsets of the real line with positive Lebesgue measure, then their sum C+D contains an interval.  We will in fact see that these two theorems are both specific instances of a more general theorem using the language of nonstandard analysis.