Schnirelmann density
In
mathematics, the
Schnirelmann density of a
subset A of the
set N of non-negative
integers is defined as follows: for each integer
n > 0, let
Then, the Schnirelmann density of
A is
The Schnirelmann density is named after
Russian mathematician L. G. Schnirelmann, who was the first to study it; the Schnirelmann density function
σ has the following properties:
- For all n, A(n) > n . σA.
- σA = 1 iff A ⊇ N.
- If 1 ∉ A, then σA = 0.
- If 0 ∈ A ∩ B, then σ(A + B) ≥ σA + σB - σA . σB
- If σA + σB ≥ 1, then σ(A + B) = 1.
- If σA > 0, then A is an additive basis.
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