Exercise 17.5.19. (a) Show that absolute value does not produce a well-defined function from Z7 to Z7. That is, show there exist a, b € Z, such that [a]7 = [b]7, but [|a|]7 # [[bl]7. (b) Show that part (a) is true for every n > 2. That is, show that absolute value does not provide a well-defined function from Z₁ to Zn
Exercise 17.5.19. (a) Show that absolute value does not produce a well-defined function from Z7 to Z7. That is, show there exist a, b € Z, such that [a]7 = [b]7, but [|a|]7 # [[bl]7. (b) Show that part (a) is true for every n > 2. That is, show that absolute value does not provide a well-defined function from Z₁ to Zn
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please do part A and B
![**Exercise 17.5.19.**
(a) Show that absolute value does not produce a well-defined function from \( \mathbb{Z}_7 \) to \( \mathbb{Z}_7 \). That is, show there exist \( a, b \in \mathbb{Z} \), such that
\[ [a]_7 = [b]_7, \text{ but } [|a|]_7 \neq [|b|]_7. \]
(b) Show that part (a) is true for every \( n > 2 \). That is, show that absolute value does not provide a well-defined function from \( \mathbb{Z}_n \) to \( \mathbb{Z}_n \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e817a-9b32-4eeb-b8fc-5dd7ffde6479%2Fea0e1126-9f1d-453d-86fb-da0041329862%2F9xoyc2r_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise 17.5.19.**
(a) Show that absolute value does not produce a well-defined function from \( \mathbb{Z}_7 \) to \( \mathbb{Z}_7 \). That is, show there exist \( a, b \in \mathbb{Z} \), such that
\[ [a]_7 = [b]_7, \text{ but } [|a|]_7 \neq [|b|]_7. \]
(b) Show that part (a) is true for every \( n > 2 \). That is, show that absolute value does not provide a well-defined function from \( \mathbb{Z}_n \) to \( \mathbb{Z}_n \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
