# Category:Cantor Set

This category contains results about Cantor Set.

Define, for $n \in \N$, subsequently:

$\map k n := \dfrac {3^n - 1} 2$
$\displaystyle A_n := \bigcup_{i \mathop = 1}^{\map k n} \openint {\frac {2 i - 1} {3^n} } {\frac {2 i} {3^n} }$

Since $3^n$ is always odd, $\map k n$ is always an integer, and hence the union will always be perfectly defined.

Consider the closed interval $\closedint 0 1 \subset \R$.

Define:

$\mathcal C_n := \closedint 0 1 \setminus A_n$

The Cantor set $\mathcal C$ is defined as:

$\displaystyle \mathcal C = \bigcap_{n \mathop = 1}^\infty \mathcal C_n$

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Cantor Set"

The following 4 pages are in this category, out of 4 total.