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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.

 


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