# sumset

Sometimes called the ‘big union,’ the sumset of a set $$A$$ is the set of the elements of the elements of $$A$$, i.e., the union of its elements. In set-theoretic notation this is

$\bigcup A = \left\{x \,\left| \,\exists y (x \in y \mbox{ and } y \in A \right.\right\}$

It is an axiom of formal set theory that for any set $$A$$ the sumset of $$A$$ exists.