Asymetric Cantor set
The Cantor set can be developed in an asymetric way.
Explanation
The asymetric Cantor set is built by removing the second quarter at each iteration.
Step 0 Step 1 Step 2 Step 3 Step 4
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 progression, as it consists of
There are no non-zero intervals left.
Endpoints
Since each step removes a finite number of intervals and the number of steps is countable, the set of endpoints is countable.
Cardinality
The whole Cantor set is uncountable, although the set of endpoints is countable. The Cantor set has the same cardinality as the interval [0,1] and so as the set of real numbers.