Cantor set (nonfiction): Difference between revisions
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[[File:Cantor set 4 iterations.svg.png|thumb|Four iterations of the Cantor set.]]In [[Mathematics (nonfiction)|mathematics]], the '''Cantor set''' is a set of points lying on a single line segment that has a number of remarkable and deep properties. | [[File:Cantor set 4 iterations.svg.png|thumb|Four iterations of the Cantor set.]]In [[Mathematics (nonfiction)|mathematics]], the '''Cantor set''' is a set of points lying on a single line segment that has a number of remarkable and deep properties. | ||
It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician [[Georg Cantor (nonfiction)|Georg Cantor]] in 1883. | It was discovered in 1874 by [[Henry John Stephen Smith (nonfiction)|Henry John Stephen Smith]] and introduced by German mathematician [[Georg Cantor (nonfiction)|Georg Cantor]] in 1883. | ||
Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. | Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. | ||
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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. | 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. | ||
== In the News == | |||
<gallery> | |||
</gallery> | |||
== Fiction cross-reference == | |||
* [[Crimes against mathematical constants]] | |||
* [[Gnomon algorithm]] | |||
* [[Gnomon Chronicles]] | |||
* [[Mathematics]] | |||
* [[The Sigil (crime fighter)]] | |||
== Nonfiction cross-reference == | |||
* [[Georg Cantor (nonfiction)]] | |||
* [[Set theory (nonfiction)]] | |||
* [[Henry John Stephen Smith (nonfiction)]] | |||
External links: | |||
* [https://en.wikipedia.org/wiki/Cantor_set Cantor set] @ Wikipedia | |||
[[Category:Mathematics (nonfiction)]] | [[Category:Mathematics (nonfiction)]] | ||
[[Category:Set theory (nonfiction)]] | [[Category:Set theory (nonfiction)]] | ||
Latest revision as of 12:50, 16 March 2018
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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.
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.
In the News
Fiction cross-reference
- Crimes against mathematical constants
- Gnomon algorithm
- Gnomon Chronicles
- Mathematics
- The Sigil (crime fighter)
Nonfiction cross-reference
External links:
- Cantor set @ Wikipedia