Definition
A subset A of positive integers has natural density (or asymptotic density) α, where
- 0 ≤ α ≤ 1,
if the proportion of elements of A among all natural numbers from 1 to n is asymptotic to α as n tends to infinity.
More explicitly, if one defines for any natural number n the counting function a(n) as the number of elements of A less than or equal to n, then the natural density of A being α exactly means that
- a(n)/n → α as n → +∞.
Read more about this topic: Natural Density
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