  A numerical set $S$ is a cofinite subset of $\mathbb{N}$ which contains $0$.
We use the natural bijection between numerical sets and Young diagrams to
define a numerical set $\widetilde{S}$, such that their Young diagrams are
complements. We determine various properties of $\widetilde{S}$, particularly
with an eye to closure under addition (for both $S$ and $\widetilde{S}$), which
promotes a numerical set to become a numerical semigroup.
