Asymptotic density

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Template:Density notion

Definition

Let be a subset of the set of natural numbers. The asymptotic density or natural density of is defined as the following quantity, if well-defined:

.

The asymptotic density need not be well-defined. However, the limit superior and limit inferior of the above sequence are always well-defined, and these are termed respectively the upper asymptotic density and lower asymptotic density.

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