## Problem 6Consider the subset \( C_0 = [0, 1] \subseteq \mathbb{R} \). Recursively, define the sets\[C_{n+1} = \frac{C_n}{3} \cup \left( \frac{2}{3} + \frac{C_n}{3} \right),\]for \( n \geq 1 \), where, if we let \( A = [a, b] \), then the notation \( A/3 \) describes the interval \([a/3, b/3]\) and the notation \( A + 2/3 \) describes the interval \([a + 2/3, b + 2/3]\).(a) Describe and draw the sets \( C_1, C_2, C_3 \) and \( C_4 \) as a union of explicit intervals.(b) Show that the intersection \( \bigcap_{n=1}^{\infty} C_n \) is non-empty.

(a). Draw the set c1,c2,c3 and c4 as a unique integers. cn+1=cn3∪23+cn3c1= c03∪23+c03c1=0,13∪23,1…

Problem 6. Consider the subset Co = [0, 1]C R. Recursively, define the sets Cn+1 = 3 2, Cn + 3 [a, b], then the notation A/3 describes the interval for n > 1, where, if we let A = [a/3, 6/3] and the notation A + 2/3 describe the interval [a + 2/3,6+2/3]. (a) Describe and draw the sets C1, C2, C3 and C4 as a union of explicit intervals. (b) Show that the intersection NCn is non-empty.

Problem 6. Consider the subset Co = [0, 1]C R. Recursively, define the sets Cn+1 = 3 2, Cn + 3 [a, b], then the notation A/3 describes the interval for n > 1, where, if we let A = [a/3, 6/3] and the notation A + 2/3 describe the interval [a + 2/3,6+2/3]. (a) Describe and draw the sets C1, C2, C3 and C4 as a union of explicit intervals. (b) Show that the intersection NCn is non-empty.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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