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Exercise 14.4.22. Let o be a permutation in S,. (a) Show that there exists an integer k > 1 such that ok = o. (b) Show that there exists an integer l > 1 such that o' = o-1. (c) Let K be the set of all integers k > 1 such that ok = o. Show that K is an infinite set (that is, K has an infinite number of elements). (d) Let L be the set of all integers l>1 such that of = o-1. Show that L is an infinite set. (e) What is the relationship between the sets K and L?

Exercise 14.4.22. Let o be a permutation in S,. (a) Show that there exists an integer k > 1 such that ok = o. (b) Show that there exists an integer l > 1 such that o' = o-1. (c) Let K be the set of all integers k > 1 such that ok = o. Show that K is an infinite set (that is, K has an infinite number of elements). (d) Let L be the set of all integers l>1 such that of = o-1. Show that L is an infinite set. (e) What is the relationship between the sets K and L?

Advanced Engineering Mathematics
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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Exercise 14.4.22. Let o be a permutation in S,. (a) Show that there exists an integer k >1 such that ok = o. (b) Show that there exists an integer l > 1 such that o = o-1. (c) Let K be the set of all integers k > 1 such that ok is an infinite set (that is, K has an infinite number of elements). = o. Show that K (d) Let L be the set of all integers l > 1 such that o = o-1. Show that L is an infinite set. (e) What is the relationship between the sets K and L?
Transcribed Image Text:Exercise 14.4.22. Let o be a permutation in S,. (a) Show that there exists an integer k >1 such that ok = o. (b) Show that there exists an integer l > 1 such that o = o-1. (c) Let K be the set of all integers k > 1 such that ok is an infinite set (that is, K has an infinite number of elements). = o. Show that K (d) Let L be the set of all integers l > 1 such that o = o-1. Show that L is an infinite set. (e) What is the relationship between the sets K and L?
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