2. Recall that the characteristic function of a set E is defined as I is in E 1, Xe(z) = { 0, z is not in E Let E be the set of rational numbers in [0,1]. Show that Xe is not continuous on E. Hint: Assume it is and Use the IVT to get a contradiction.
2. Recall that the characteristic function of a set E is defined as I is in E 1, Xe(z) = { 0, z is not in E Let E be the set of rational numbers in [0,1]. Show that Xe is not continuous on E. Hint: Assume it is and Use the IVT to get a contradiction.
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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#2. Thanks. 11.2
![2. Recall that the characteristic function of a set E is defined as
r is in E
1,
Xe(1) = { 0, z is not in E
Let E be the set of rational numbers in [0, 1]. Show that Xe is not continuous on E. Hint:
Assume it is and Use the IVT to get a contradiction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbb66fa7-7c22-4982-a22f-aaed542f65b3%2F768c8e13-accb-4563-9ed5-ebd49890089b%2Fmd4s4m9_processed.png&w=3840&q=75)
Transcribed Image Text:2. Recall that the characteristic function of a set E is defined as
r is in E
1,
Xe(1) = { 0, z is not in E
Let E be the set of rational numbers in [0, 1]. Show that Xe is not continuous on E. Hint:
Assume it is and Use the IVT to get a contradiction.
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