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2. Consider the following set of linear polynomials with rational coefficients: E = {ar+bla.be Q. a 0} (a). Prove that E₁ is countably infinite. (b). In general, let E, denote the set of polynomials of degree n with rational coefficients. Prove that. En is countably infinite for all n ≥ 0.

2. Consider the following set of linear polynomials with rational coefficients: E = {ar+bla.be Q. a 0} (a). Prove that E₁ is countably infinite. (b). In general, let E, denote the set of polynomials of degree n with rational coefficients. Prove that. En is countably infinite for all n ≥ 0.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.1: Polynomials Over A Ring
Problem 13E
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2. Consider the following set of linear polynomials with rational coefficients: E₁ {ar+ba.be Q. a 0} = (a). Prove that E₁ is countably infinite. (b). In general, let E, denote the set of polynomials of degree n. with rational coefficients. Prove that. En is countably infinite for all n ≥ 0.
Transcribed Image Text:2. Consider the following set of linear polynomials with rational coefficients: E₁ {ar+ba.be Q. a 0} = (a). Prove that E₁ is countably infinite. (b). In general, let E, denote the set of polynomials of degree n. with rational coefficients. Prove that. En is countably infinite for all n ≥ 0.
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