  A set $A\subseteq\mathbb N$ is called $complete$ if every sufficiently large
integer can be written as the sum of distinct elements of $A$. In this paper we
present a new method for proving the completeness of a set, improving results
of Cassels ('60), Zannier ('92), Burr, Erd\H{o}s, Graham, and Li ('96), and
Hegyv\'ari ('00). We also introduce the somewhat philosophically related notion
of a $dispersing$ set and refine a theorem of Furstenberg ('67).
