ii) (Volterra set) Repeat the Cantor construction starting with the interval [0,1]. This time remove, in the k-iteration, an open interval of length 1/4k from the center of the remaining closed intervals to obtain SCV (4). ii-1) Draw the first 3 iterative steps of the construction of SCV (4) in detail. ii-2) Using the argument above or from Section 11.1 of the book (pages 330-332), compute the length of this Cantor-like set SCV (4), and prove that contains no intervals.
ii) (Volterra set) Repeat the Cantor construction starting with the interval [0,1]. This time remove, in the k-iteration, an open interval of length 1/4k from the center of the remaining closed intervals to obtain SCV (4). ii-1) Draw the first 3 iterative steps of the construction of SCV (4) in detail. ii-2) Using the argument above or from Section 11.1 of the book (pages 330-332), compute the length of this Cantor-like set SCV (4), and prove that contains no intervals.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 78E
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