How is the Cantor set constructed from the unit interval?
By intersecting sets formed by successively removing open middle thirds.
Which digits appear in ternary expansions of Cantor set numbers?
Only the digits 0 and 2 appear.
What happens at each stage in the successive middle-third removal process?
The open middle third of every surviving closed interval is removed.
What is the form of the surviving set F_n at stage n?
It is the union of 2^n closed intervals.
Which points belong to every F_n and the Cantor set F?
0, 1/3, 2/3, and 1 belong to every F_n and the Cantor set F.
What does the Cantor set contain regarding intervals?
It contains no nonempty interval.
What is the length of the stage-n Cantor set?
Why is the Cantor set large in cardinality despite being geometrically thin?
Because it has as many points as the unit interval.
Answer 8 questions on The Cantor Set.
1. How is the Cantor set defined in the middle-third construction?
2. Which ternary-expansion property characterizes membership in the Cantor set?
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