Let x ∈ [0, 1] andφ(x) =1 if x ∈ C ∩ Q−2 if x ∈ C ∩ Qc−3 if x ∈ [0, 1] \ Cwhere C is the Cantor set (recall Example 1.1.7) and Q is the set of rational numbers. FindR 10φ. Question 1. Let r E [0, 1] and1 if rECnQ$(r) = {-2 if a €CNQ-3 if a E [0, 1] \C1where C is the Cantor set (recall Example 1.1.7) and Q is the set of rational mumbers. Find

Given the set x∈0,1 and ϕx=1 if x∈C∩ℚ-2 if x∈C∩ℚc-3 if x∈0,1\ℚ.

Answered: Question 1. Let r E [0, 1] and 1 if…

Question 1. Let r E [0, 1] and 1 if reCnQ (r) = {-2 if IECNQ -3 if z € [0, 1] \C where C is the Cantor set (recall Example 1.1.7) and Q is the set of rational numbers. Find

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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Question

Let x ∈ [0, 1] and

φ(x) =



1 if x ∈ C ∩ Q
−2 if x ∈ C ∩ Qc
−3 if x ∈ [0, 1] \ C

where C is the Cantor set (recall Example 1.1.7) and Q is the set of rational numbers. Find
R 1
0
φ.

Question 1. Let r E [0, 1] and
1 if rECnQ
$(r) = {-2 if a €CNQ
-3 if a E [0, 1] \C
1
where C is the Cantor set (recall Example 1.1.7) and Q is the set of rational mumbers. Find

Expert Solution

Step 1

Given the set $x \in [0, 1]$ and

$ϕ (x) = \{\begin{cases} 1 i f x \in C \cap ℚ \\ - 2 i f x \in C \cap ℚ^{c} \\ - 3 i f x \in [0, 1] \ ℚ \end{cases} .$

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