Abstract
A set of positive integers is an asymptotic basis of order h if every sufficiently large integer can be expressed as a sum of h or fewer elements of the set and if h is the smallest number for which this is true. The restricted order of an asymptotic basis A is the least integer h, if it exists, such that every sufficiently large integer is the sum of h or fewer distinct elements of A. In this paper, we prove that if B is a set with lower asymptotic density d_(B)>1/2, then the restricted order of B is 2. Furthermore, we will prove that 1/2 is optimal.
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