Density
It follows from the fact that sum-free sequences are small that they have zero Schnirelmann density; that is, if is defined to be the number of sequence elements that are less than or equal to, then . Erdős (1962) showed that for every sum-free sequence there exists an unbounded sequence of numbers for which where is the golden ratio, and he exhibited a sum-free sequence for which, for all values of, .
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