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Introduction to Real Analysis

Introduction to Real Analysis. Dr. Weihu Hong Clayton State University 10 / 21 /2008. The Cantor Set. What is the Cantor set? Please check out at my website at http://cims.clayton.edu/whong/tools/CantorSet.htm What can you say about the Cantor Set?. Properties of the Cantor Set.

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Introduction to Real Analysis

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  1. Introduction to Real Analysis Dr. Weihu Hong Clayton State University 10/21/2008

  2. The Cantor Set • What is the Cantor set? Please check out at my website at http://cims.clayton.edu/whong/tools/CantorSet.htm • What can you say about the Cantor Set?

  3. Properties of the Cantor Set • It is compact and nonempty. • It contains all the end points of the closed intervals

  4. Properties of the Cantor Set • Every point of the Cantor set is a limit point of the Cantor set. • The sum of the lengths of the intervals removed is 1. • The Cantor set contains no intervals. • If for each xє[0,1], is the ternary expansion of x, then

  5. Properties of the Cantor Set • The Cantor set is uncountable.

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