The Cantor Set

The Cantor set is important for understanding Topology (open and closed sets) and measure.

Let $C_{0}$ be the closed interval $[0, 1]$ and define $C_{1}$ to be the set that results when the open middle third is removed:

[

C_{1} = C_{0} ∖ ? = ? \cup ?

]

This process continued gives us the Cantor set:

C = ⋂_{n = 0}^{\infty} C_{n}

Or alternatively:

[

C = [0, 1] ∖ ((\frac{1}{3}, \frac{2}{3}) \cup (?, ?) \cup (?, ?) \cup . . .)

]

Below are some properties of the Cantor set, with explanations on the reverse side.

The cantor set...

25.02.2021