 Upper asymptotic density (source code)

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= Upper asymptotic density
{title2=$\overline d(A)$}

= Upper natural density
{synonym}

For a subset $A$ of the positive integers, its upper asymptotic density is $\overline d(A)=\limsup_{N\to\infty}|A\cap\{1,\ldots,N\}|/N$. Unlike <natural density>, it always exists. If <natural density> exists, the two agree. Positive upper asymptotic density suffices for the <Szemerédi theorem>.

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