Cantor set
Sign in to saveAlso known as Cantor sets, Cantor ternary set
fractal and set of points on a line segment
Wikidata facts
- Instance of
- null set
- Part of
- unit interval
- Named after
- Georg Cantor
- Image
- Cantor-like Column Capital Ile de Philae Description d'Egypte 1809.jpg
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- Commons category
- Cantor sets
- different from
- Cantor space
- maintained by WikiProject
- WikiProject Mathematics
- set cardinality
- cardinality of the continuum
via Wikidata · CC0
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Encyclopedic overview
Seven iterations of the Cantor set's construction. In mathematics, the Cantor set is a self-similar set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and mentioned by German mathematician Georg Cantor in 1883. As it contrasts with a linear continuum, the Cantor set has been called the Cantor discontinuum.
Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. The most common construction is the Cantor ternary set, built by removing the middle third of a line segment and then repeating the process with the remaining shorter segments. Cantor mentioned this ternary construction only in passing, as an example of a perfect set that is nowhere dense.
Excerpted from Wikipedia’s “Cantor set” article, available under the CC BY-SA 4.0 licence.