## 5.2. Compact and Perfect Sets

### Definition 5.2.12: Cantor Middle Third Set

Start with the unit interval

Remove from that set the middle third and setS_{0}= [0, 1]

Remove from that set the two middle thirds and setS_{1}=S_{0}\ (1/3, 2/3)

Continue in this fashion, whereS_{2}=S_{1}\ { (1/9, 2/9) (7/9, 8/9) }

Then theS_{n+1}=S_{n}\ { middle thirds of subintervals ofS_{n}}

**Cantor set**is defined as**C**For a list of properties of the Cantor set, look at the theory of compact and perfect sets.=CS_{n}