For each of the following sets, is it countable or uncountable? Briefly explain why. Your explanation should be something like: "There is a surjective function from Z² to the set (with your function written explicitly). Since Z² is countable, the set is countable. 1. R XZ 2. Z[i] = {a + bi | a, b = Z²} 3. {| p is a prime number}. NT 4. {x ER | x = or x = 2 ne 3 for some ne Z}. 5. M₂ (R), the set of 2 × 2 matrices over R. 6. S = {Straight lines in R²}.

For each of the following sets, is it countable or uncountable? Briefly explain why. Your explanation should be something like: "There is a surjective function from Z² to the set (with your function written explicitly). Since Z² is countable, the set is countable. 1. R XZ 2. Z[i] = {a + bi | a, b = Z²} 3. {| p is a prime number}. NT 4. {x ER | x = or x = 2 ne 3 for some ne Z}. 5. M₂ (R), the set of 2 × 2 matrices over R. 6. S = {Straight lines in R²}.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 23E: Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove...

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