# Category:Cantor Set

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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.

### C

## Pages in category "Cantor Set"

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