√2: s, 1€ Q}. Show that K satisfies the following: K, then x₁ + x₂ € K and X₁ X₂ € K. 9. Let K:= {s + (a) If x₁, x₂ (b) If x 0 and x € K, then 1/x € K. (Thus the set K is a sub field of R. With the order inherited from R, the set K is an ordered field that lies between Q and R.)
√2: s, 1€ Q}. Show that K satisfies the following: K, then x₁ + x₂ € K and X₁ X₂ € K. 9. Let K:= {s + (a) If x₁, x₂ (b) If x 0 and x € K, then 1/x € K. (Thus the set K is a sub field of R. With the order inherited from R, the set K is an ordered field that lies between Q and R.)
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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![9. Let K = {s+t√2: s, 1 € Q}. Show that K satisfies the following:
(a) If x₁, x₂ € K, then x₁ + x₂ € K and x₁x₂ € K.
(b) If x #0 and x € K, then 1/x € K.
(Thus the set K is a sub field of R. With the order inherited from R, the set K is an ordered field
that lies between Q and R.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9013942-fe12-41e5-9001-e2df564b9c37%2F1a394672-bae8-4204-a7d1-4774682833d1%2Fqaz5j6_processed.png&w=3840&q=75)
Transcribed Image Text:9. Let K = {s+t√2: s, 1 € Q}. Show that K satisfies the following:
(a) If x₁, x₂ € K, then x₁ + x₂ € K and x₁x₂ € K.
(b) If x #0 and x € K, then 1/x € K.
(Thus the set K is a sub field of R. With the order inherited from R, the set K is an ordered field
that lies between Q and R.)
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