Let A = { n - m : neN, me N, m > n}. (a) Prove that inf A = 0. (b) Prove that sup A = 1.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 4E: 4. Let , where is nonempty. Prove that a has left inverse if and only if for every subset of .
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Let A = {
n
-
m
: neN, m € N, m> n}.
(a) Prove that inf A = 0.
(b) Prove that sup A = 1.
Transcribed Image Text:Let A = { n - m : neN, m € N, m> n}. (a) Prove that inf A = 0. (b) Prove that sup A = 1.
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