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Small set

From Number

Revision as of 17:54, 7 May 2009 by Vipul (talk | contribs) (Created page with '{{natural number subset property}} ==Definition== A subset <math>S</math> of the set of natural numbers <math>\mathbb{N}</math> is termed a '''small set''' if the sum of the re...')

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Template:Natural number subset property

Definition

A subset $S$ of the set of natural numbers $\mathbb {N}$ is termed a small set if the sum of the reciprocals of the elements of $S$ converges.

Note that the property of being a small set is unchanged upon the addition or removal of finitely many elements.

Relation with other properties

Stronger properties

Finite subset of the natural numbers.

Opposite properties

Large set

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