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1. Prove, by giving a bijection to or from N, that the following sets are countable. You do not need to prove that the functions you are defining are bijections. (i) The set of integers with remainder 2 upon division by 8. (ii) {x € (0, ∞) : cos x = 0}, where (0, ∞) = {x € R: x>0}.

1. Prove, by giving a bijection to or from N, that the following sets are countable. You do not need to prove that the functions you are defining are bijections. (i) The set of integers with remainder 2 upon division by 8. (ii) {x € (0, ∞) : cos x = 0}, where (0, ∞) = {x € R: x>0}.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 24E
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1. Prove, by giving a bijection to or from N, that the following sets are countable. You do not need to prove that the functions you are defining are bijections. (i) The set of integers with remainder 2 upon division by 8. (ii) {x € (0, ∞): cos x = 0}, where (0, ∞) = {x € R: x>0}.
Transcribed Image Text:1. Prove, by giving a bijection to or from N, that the following sets are countable. You do not need to prove that the functions you are defining are bijections. (i) The set of integers with remainder 2 upon division by 8. (ii) {x € (0, ∞): cos x = 0}, where (0, ∞) = {x € R: x>0}.
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