Schnirelmann density - Revision history

Vipul at 21:18, 6 May 2009

2009-05-06T21:18:23Z

← Older revision		Revision as of 21:18, 6 May 2009
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	<math>\inf_{n \in \mathbb{N}_0} \frac{S \cap \{ 0,1, \dots, n \}}{n + 1}</math>.		<math>\inf_{n \in \mathbb{N}_0} \frac{S \cap \{ 0,1, \dots, n \}}{n + 1}</math>.

			Note that Schnirelmann density is highly sensitive to initial values, and for this reason, the value of the Schnirelmann density depends on whether we are treating the set as a subset of <math>\mathbb{N}</math> or of <math>\mathbb{N}_0</math>.

	==Related notions==		==Related notions==

Vipul at 21:17, 6 May 2009

2009-05-06T21:17:14Z

← Older revision		Revision as of 21:17, 6 May 2009
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	==Related notions==		==Related notions==

	* [[~~Asymptotic Schnirelmann~~ density]]		* [[Upper asymptotic density]]
			* [[Lower asymptotic density]]
	==Facts==		==Facts==

	* [[Mann's theorem]]		* [[Mann's theorem]]
	* [[Schnirelmann's theorem on Goldbach's conjecture]]		* [[Schnirelmann's theorem on Goldbach's conjecture]]

Vipul: Created page with '{{density notion}} ==Definition== Let $S$ be a subset of the set $\mathbb{N}$ of natural numbers. The '''Schnirelmann density''' of $S$ is defi...'

2009-05-06T21:08:25Z

Created page with '{{density notion}} ==Definition== Let <math>S</math> be a subset of the set <math>\mathbb{N}</math> of natural numbers. The '''Schnirelmann density''' of <math>S</math> is defi...'

New page

{{density notion}}

==Definition==

Let <math>S</math> be a subset of the set <math>\mathbb{N}</math> of natural numbers. The '''Schnirelmann density''' of <math>S</math> is defined as:

<math>\inf_{n \in \mathbb{N}} \frac{S \cap \{ 1,2, \dots, n \}}{n}</math>.

The definition can be modified to consider subsets of <math>\mathbb{N}_0</math>, the natural numbers with zero. the '''Schnirelmann desity''' of <math>\mathbb{N}_0</math> is defined as:

<math>\inf_{n \in \mathbb{N}_0} \frac{S \cap \{ 0,1, \dots, n \}}{n + 1}</math>.

==Related notions==

* [[Asymptotic Schnirelmann density]]

==Facts==

* [[Mann's theorem]]
* [[Schnirelmann's theorem on Goldbach's conjecture]]

Schnirelmann density - Revision history

Vipul at 21:18, 6 May 2009

Vipul at 21:17, 6 May 2009

Vipul: Created page with '{{density notion}} ==Definition== Let S be a subset of the set \mathbb{N} of natural numbers. The '''Schnirelmann density''' of S is defi...'

Vipul: Created page with '{{density notion}} ==Definition== Let $S$ be a subset of the set $\mathbb{N}$ of natural numbers. The '''Schnirelmann density''' of $S$ is defi...'