Weakly Independent

An infinite sequence $\{a_i\}$ of Positive Integers is called weakly independent if any relation $\sum \epsilon_i a_i$ with $\epsilon_i=0$ or $\pm 1$ and $\epsilon_i=0$, except finitely often, Implies $\epsilon_i=0$ for all $i$.

See also Strongly Independent

References

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 136, 1994.