The Cantor ternary set is created by repeatedly deleting the open middle thirds of a set of line segments. One starts by deleting the open middle third (1⁄3, 2⁄3) from the interval [0, 1], leaving two line segments: [0, 1⁄3] ∪ [2⁄3, 1]. Next, the open middle third of each of these remaining segments is deleted, leaving four line segments: [0, 1⁄9] ∪ [2⁄9, 1⁄3] ∪ [2⁄3, 7⁄9] ∪ [8⁄9, 1]. This process is continued ad infinitum, where the nth set is
The Cantor ternary set contains all points in the interval [0, 1] that are not deleted at any step in this infinite process.
The first six steps of this process are illustrated below.
An explicit formula for the Cantor set is
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