Cantor Set

This task leads to the generation of finite geometric series with a common ratio less than one as a means to explore properties of the Cantor Set. The Cantor Set is a fascinating set with many intriguing properties. It contains uncountably many points, which means that there are "as many" points in it as on the real line, yet the set contains no intervals of real numbers and it has length zero. All that is necessary to show that it has length zero is to look at what happens to a geometric series as we add more and more terms.
Resource ID#: 42317 Type: Problem-Solving Task
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General Information

Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators educators, Students , Parents
Keywords: cantor set, cantor, set, fractal, interval, fraction, infinite, cpalms, icpalms, illustrativemathematics.org, illustrative mathematics, tasks, mathematics, math, Florida standards, resource, free, freely available, problems-based learning, student activities
Instructional Component Type(s): Problem-Solving Task
Resource Collection: Illustrative Mathematics

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