Cantor set
The Cantor set is a subset of the real numbers in the unit interval.
Explanation
The Cantor set is built by removing the middle third at each iteration.
Step 0 Step 1 Step 2 Step 3 Step 4 Step 5
Intervals
Each step removes a finite number of intervals and the number of steps is countable. The gray color shows the intervals that are deleted in every following step. It forms a geometric series, as it consists of
There are no non-zero intervals left.
HistoryThe German mathematician Georg Cantor (1845 - 1918) is considered the founder of set theory. |