Karl Jones: Created page with "In mathematics, the '''Cantor set''' is a set of points lying on a single line segment that has a number of remarkable and deep properties. == Description == It was disc..."

2016-10-14T15:06:48Z

Created page with "In mathematics, the '''Cantor set''' is a set of points lying on a single line segment that has a number of remarkable and deep properties. == Description == It was disc..."

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In [[mathematics]], the '''Cantor set''' is a set of points lying on a single line segment that has a number of remarkable and deep properties.

== Description ==

It was discovered in 1874 by [[Henry John Stephen Smith]] and introduced by German mathematician [[Georg Cantor]] in 1883.

Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology.

Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle thirds of a line segment.

Cantor himself mentioned the ternary construction only in passing, as an example of a more general idea, that of a [[perfect set]] that is [[Nowhere dense set|nowhere dense]].

== See also ==

* [[Antoine's necklace]]
* [[Cantor function]]
* [[Cantor cube]]
* [[Hexagrams (I Ching)]]
* [[Koch snowflake]]
* [[Knaster–Kuratowski fan]]
* [[List of fractals by Hausdorff dimension]]
* [[Nowhere dense set]]
* [[Perfect set]]

== External links ==

* [https://en.wikipedia.org/wiki/Cantor_set Cantor set] @ Wikipedia

[[Category:Mathematics]]
[[Category:Set theory]]

Cantor set - Revision history

Karl Jones: Created page with "In mathematics, the '''Cantor set''' is a set of points lying on a single line segment that has a number of remarkable and deep properties. == Description == It was disc..."