(a) Write down an example of an element of A that is not one of the functions a above. (b) Prove that A is a group with the operation of function composition.
(a) Write down an example of an element of A that is not one of the functions a above. (b) Prove that A is a group with the operation of function composition.
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 A be the set of all permutations f: Z Z such that there exists a positive integer
n for which, for all i e Z, we have
f(i+n) = f(i) +n.
For example, for each k E Z, the "add k" function a, : Z Z defined by a, (0-i+k
lies in A.
(a) Write down an example of an element of A that is not one of the functions a
above.
(b) Prove that A is a group with the operation of function composition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8e908be-d8aa-4058-95d4-afe421ebfea7%2F5be146b8-44bd-4a43-aef0-d73b567ee8ff%2F4gau4jj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let A be the set of all permutations f: Z Z such that there exists a positive integer
n for which, for all i e Z, we have
f(i+n) = f(i) +n.
For example, for each k E Z, the "add k" function a, : Z Z defined by a, (0-i+k
lies in A.
(a) Write down an example of an element of A that is not one of the functions a
above.
(b) Prove that A is a group with the operation of function composition.
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