Definition:
Cantor Middle Third Set
Start with the unit interval
Remove from that set the middle third and set
Remove from that set the two middle thirds and set
- S 2 = S 1 \ { (1/9, 2/9)
(7/9, 8/9) }
Continue in this fashion, where
- S n+1 = S n \
{ middle thirds of subintervals of
S n }
Then the Cantor set C is defined as
- C =
S n
For a list of properties of the Cantor set, look at the theory of compact and perfect
sets.
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