(a) Show that the total length of all the intervals that are removed is $1 .$ Despite that, the Cantor set contains infinitely many numbers. Give examples of some numbers in the Cantor set.(b) The Sierpinski carpet is a two-dimensional counterpart of the Cantor set. It is constructed by removing the center one-ninth of a square of side $1,$ then removing the centers of the eight smaller remaining squares, and so on. (The figure shows the first three steps of the construction.) Show that the sum of the areas of the removed squares is $1 .$ This implies that the Sierpinski carpet has area 0

(a) Show that the total length of all the intervals that are removed is $1 .$ Despite that, the Cantor set contains infinitely many numbers. Give examples of some numbers in the Cantor set.(b) The Sierpinski carpet is a two-dimensional counterpart of the Cantor set. It is constructed by removing the center one-ninth of a square of side $1,$ then removing the centers of the eight smaller remaining squares, and so on. (The figure shows the first three steps of the construction.) Show that the sum of the areas of the removed squares is $1 .$ This implies that the Sierpinski carpet has area 0

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Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Complex Numbers

Section: Chapter Questions

Problem 14PS

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