  An additive system for the nonnegative integers is a family (A_i)_{i\in I} of
sets of nonnegative integers with 0 \in A_i for all i \in I such that every
nonnegative integer can be written uniquely in the form \sum_{i\in I} a_i with
a_i \in A_i for all i and a_i \neq 0 for only finitely many i. In 1956, de
Bruijn proved that every additive system is constructed from an infinite
sequence (g_i)_{i \in \N} of integers with g_i \geq 2 for all i, or is a
contraction of such a system. This paper gives a complete classification of the
"uncontractable" or "indecomposable" additive systems, and also considers
limits and stability of additive systems.
