- categories: Real Analysis, Definition
The Cantor ternary set 𝐶 is created by iteratively deleting the open middle third from a set of line segments.
Consequence of these sets are nested and compact, so there intersection is not empty
There are as many points in the Cantor set as there are in the interval [0,1]
Numbers that don’t contain 1 in ternary expansion
Properties
- Measure of Cantor set is 0 (proportion)
- Cantor set is a Perfect set but has no interior
- Cantor set is Complete metric space
Fat Cantor set
Retains some “thickness” at each stage of its construction and has positive Lebesgue measure