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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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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