Cantor set

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 named after Georg Cantor. Henry John Stephen Smith discovered it in 1875, and Cantor first described it in 1883.

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 
 Fractal
 Set theory
 Smith–Volterra–Cantor set
 Cantor dust
 Menger Sponge

 Other websites 




 Cantor set at PRIME 

References

Category:Fractals
Category:Set theory