The Cantor set is a subset of real numbers with certain properties that are interesting to mathematicians. These properties relate to topology, measurement, geometry, as well as set theory. Some of them are:
- When represented geometrically, the set is a fractal, it has a Hausdorff dimension which is not an integer
- It has the same cardinality as the set of real numbers
- It is self-similar
The set is made by starting with a line segment and repeatedly removing the middle third. The Cantor set is the (infinite) set of points left over. The Cantor set is "more infinite" than the set of natural numbers (1, 2, 3, 4, etc.). This property is called uncountability. It is related to the Smith–Volterra–Cantor set and the Menger Sponge. The Cantor set is self-similar.
Related pages[change | edit source]
Other websites[change | edit source]
- Barile, Margherita and Weisstein, Eric W. "Cantor Set". Wolfram MathWorld. http://mathworld.wolfram.com/CantorSet.html. Retrieved 23 January 2012.
- Su, Francis E., et al.. "Cantor Set.". Math Fun Facts. http://www.math.hmc.edu/funfacts/ffiles/20004.3.shtml. Retrieved 23 January 2012.
- Neal Carothers. "The Cantor Set". http://personal.bgsu.edu/~carother/cantor/Cantor1.html.
- Cantor set at PRIME
- Media related to Cantor sets at Wikimedia Commons
References[change | edit source]
- "Theory of Infinite Sets". Exploratorium.edu. http://www.exploratorium.edu/complexity/CompLexicon/settheory.html. Retrieved 2012-01-27.
- Erin Chamberlain. "The Cantor Set". http://www.math.utah.edu/~erin/32103/Cantor.pdf. Retrieved 2012-01-27.
- Rupert Levene (February 13, 2009). "The Cantor set is uncountable". http://www.maths.tcd.ie/~levene/221/pdf/cantor.pdf. Retrieved 2012-01-27.