4. 5. 6. Let X be a set and let f: XX be a function. We say that f is an involution if fof idx and that f is idempotent if f f = f. (a) If f is an involution, must it be invertible? Why or why not?2 (b) If f is idempotent, must it be invertible? Why or why not? (c) If f is idempotent and x E range(f), prove that f(x) = x. Prove that [log3 536] 5. You proof must be verifiable by someone who does not have access to a scientific calculator or a logarithm table (you cannot use log3 536≈ 5.7). Define the sequence {a} by a = 2-i for i≥ 1. (a) Give the first five terms of the sequence. (b) Prove that the sequence is increasing.
4. 5. 6. Let X be a set and let f: XX be a function. We say that f is an involution if fof idx and that f is idempotent if f f = f. (a) If f is an involution, must it be invertible? Why or why not?2 (b) If f is idempotent, must it be invertible? Why or why not? (c) If f is idempotent and x E range(f), prove that f(x) = x. Prove that [log3 536] 5. You proof must be verifiable by someone who does not have access to a scientific calculator or a logarithm table (you cannot use log3 536≈ 5.7). Define the sequence {a} by a = 2-i for i≥ 1. (a) Give the first five terms of the sequence. (b) Prove that the sequence is increasing.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 7E: Prove that if f is a permutation on A, then (f1)1=f.
Related questions
Question
![4.
5.
6.
Let X be a set and let f: XX be a function. We say that f is an involution if
fof idx and that f is idempotent if f f = f.
(a) If f is an involution, must it be invertible? Why or why not?2
(b) If f is idempotent, must it be invertible? Why or why not?
(c) If f is idempotent and x E range(f), prove that f(x) = x.
Prove that [log3 536] 5. You proof must be verifiable by someone who does not
have access to a scientific calculator or a logarithm table (you cannot use log3 536≈ 5.7).
Define the sequence {a} by a = 2-i for i≥ 1.
(a) Give the first five terms of the sequence.
(b) Prove that the sequence is increasing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1542e5de-e392-4bdb-9d95-e5abdf8e6267%2F3e80a3b2-12f1-40b3-8f3c-234ec61aee1b%2Fbp1teed_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4.
5.
6.
Let X be a set and let f: XX be a function. We say that f is an involution if
fof idx and that f is idempotent if f f = f.
(a) If f is an involution, must it be invertible? Why or why not?2
(b) If f is idempotent, must it be invertible? Why or why not?
(c) If f is idempotent and x E range(f), prove that f(x) = x.
Prove that [log3 536] 5. You proof must be verifiable by someone who does not
have access to a scientific calculator or a logarithm table (you cannot use log3 536≈ 5.7).
Define the sequence {a} by a = 2-i for i≥ 1.
(a) Give the first five terms of the sequence.
(b) Prove that the sequence is increasing.
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